Click here👆to get an answer to your question ️ Obtain the differential equation of the family of circles x^2 y^2 2gx 2fy c = 0 ;Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreTo ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW Two curves `ax^22hxyby^22gx2fyc=0 and a'x^22hxy(a'ab)y^22g;x2f'yc=0`
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X^2+y^2+2gx+2fy+c=0 differential equation- If the equation x^(2) y^(2) 2gx 2fy c = 0 represents a circle with Xaxis as a diameter , and radius a, then Updated On To keep watching this video solution for FREE, Download our App Join the 2 Crores Student community now!Do you remember that the formula for a circle is math(xa)²(xb)²=r²/math?
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If the equation x^(2) y^(2) 2gx 2fy c = 0 represents a circle with Xaxis as a diameter , and radius a, then Apne doubts clear karein ab Whatsapp par bhi Try it nowSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more Circle, Equations You can clearly see the graph of a circle with the equation x^2 y^2 2gx2fyc=0 in red color If we change the values of f, g and c using their corresponding slide bars we will see that the position and size of the circle will change Let us observe how the size and position of the circle changes as we change the values of
obtain he differential equation of the family of circles x 2 y 2 2gx 2fy c 0 where g f and c are arbitary constants Mathematics TopperLearningcom lvss1aqqWhere g , f and c are arbitrary constants Given equation is ⇒ x 2 y 2 2x 4y 5 = 0 We know that for a pair of straight lines ax 2 2hxy by 2 2gx 2fy c = 0, the conditions to be satisfied is abc 2fgh af 2 bg 2 cf 2 = 0, h 2 ≥ ab, g 2 ≥ ca and f 2 ≥ bc Here we can see that h = 0 a = b = 1 ⇒ h 2 = 0 2 = 0 ⇒ ab = 11 = 1 ⇒ h 2 ≤ ab
Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeSimple and best practice solution for 4x^32hxyby^22gx2fyc=0 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework If it's not what You are looking for type in the equation solver your own equation and let us solve itX 2 y 2 2gx 2fy c = 0 (1) This equation may be written Hence (1) represents a circle whose centre is the point ( g, f), and whose radius is If g 2 f 2 > c, the radius of this circle is real If g 2 f 2 = c, the radius vanishes, i e the circle becomes a point coinciding with the point ( g, f) Such a circle is called a pointcircle
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If the equation `ax^(2)ay^(2)2gx2fyc=0` represents a pair of lines thenX 2 y 2 2gx 2fy c = 0(i) where c, g, f are constants Given, x 2 y 2 2x 10y 26 = 0 Comparing with (i) we see that the equation represents a circle with 2g = 2 The equation x^(2) y^(2) 2gx 2fy c = 0 represents a pointcircle when Updated On 144 To keep watching this video solution for FREE, Download our App Join the 2 Crores Student community now!
Consider The Family Of Circles X2 Y2 2fy 1 0 Where F Is A Parameter Thenthe Orthogonal Trajectories For This Family Is A X2 Y2 Dx 1
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IF the equation x^ (2) y^ (2) 2gx 2fy 1 = 0 represents a pair of lines, then Join the 2 Crores Student community now!In this video we will solve another non exact differential equations of type 4 by checking the exactness and then finding a suitable integrating factorSo si The general equation of second degree is a{{x}^{2}}2hxyb{{y}^{2}}2gx2fyc=0 The curve represented by this equation is a conic section or conic The nature of the conic is represented by these two quantities,
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It remains (2) F ( x, y) = y 2 6 x y 4 x 2 = 0 No, we look for what happens along lines y = m x that we substitute in (2) giving the equation x 2 ( m 2 6 m 4) = 0 This is possible with the two slopes (3) m = − 3 ± 5 As the asymptotes must pass through the center, their equations will be y − 6 / 5 = m ( x 2 / 5) The general equation of a circle is x 2 y 2 2 g x 2 f y c = 0 Whose center is at ( – g, – f) and the radius is g 2 f 2 − c 4 A quadratic equation in x and y a x 2 2 h x y b y 2 2 g x 2 f y c = 0 will represent equation of a circle if a = b and h = 0 5If equation x^2y^22hxy2gx2fyc=0 represents a circle , then the condition for the circle to pass through three quadrants but not passing through the origin is Apne doubts clear karein ab Whatsapp par bhi Try it now CLICK HERE Watch 1000 concepts & tricky questions explained!
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The equation x^(2) y^(2) 2gx 2fy c = 0 represents a pointcircle when Apne doubts clear karein ab Whatsapp par bhi Try it now CLICK HERE 1x 15x 2x Loading DoubtNut Solution for you Watch 1000 concepts & tricky questions explained!Click here👆to get an answer to your question ️ Obtain the differential equation of the family of circles x^2 y^2 2gx 2fy c = 0 ;Watch Video in App This browser does not support the video element 332 k 243 k
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The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction x^ {2}2yxy^ {2}2yc=0 x 2 2 y x y 2 2 y c = 0 This equation is in standard form ax^ {2}bxc=0 Substitute 1 for a, 2y for b, and y^ {2}2yc for c in the quadratic formula, \frac {b±\sqrt {b^ {2}4ac}} {2a}This lesson will cover a few more examples on equations of circles Example 6 Find the centre and the radius of the circle x 2 y 2 – 4x 6y – 3 = 0 Solution Comparing this with the general equation of the circle, ie x 2 y 2 2gx 2fy c = 0, we have g = –2, f = 3 and c = – 3 The centre will be (–g, –f) or (2, –3), andCalculation Comparing the above equation with x 2 y 2 2gx 2fy c = 0, we get, The equation x2 y2 2gx 2fy c = 0 always represents a circle whose centre is (g, f), that is ( 1 2 coefficient of x, 1 2 coefficient of y) and radius is g 2 f 2 − c If g2 f2 c = 0 then the radius of the circle becomes zero (degenerate circle)
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If the equation x^2y^22h x y2gx2fyc=0 represents a circle, then the condition for that circle to pass through three quadrants only but not passing through the origin is f^2> c (b) g^2>2 c >0 (d) h=0 Updated On To keep watching this video solution forComparing x 2 y 2 = 0 with the general equation ax 2 2hxy by 2 2gx 2fy c = 0, we can say that a = 1, b = 1 and all other coefficients are 0 Δ = abc 2fgh af 2 bg 2 cf 2 = 0 ∴ The equation represents a pair of straight lines Download Question With Solution PDF ››Watch Video in App This browser does not support the video element
If The Circle X 2 Y 2 2gx 2fy C 0 Is Touched By Y X At P Such That O P 6sqrt 2 Then The Value Of C Is 36 B 144 C 72 D None Of These
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This browser does not support the video element Step by step solution by experts to help you in doubt clearance & scoring excellent marks in examsJun 15,21 The order of the differential equation x2y22gx2fyc=0, isa)1b)2c)3d)4Correct answer is option 'C' Can you explain this answer?> If you don't, learn it here Writing standard equation of a circle Analytic geometry (video) Khan Academy mathx²y²2gx2fyc=0/math is merely
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The order of the differential equation whose solution is x^2 y^2 2gx 2fy c = 0 isIf x^2y^22gx2fyc=0 is equation of smallest circle is passing through (1,2) and touches line xy7=0 then value of (g2f3c) is Answers 1 Show answers Another question on Math Math, 1000 H€¥α £θlkš the mean of 6 numbers is 42if one number is excludedX ^ 2 y ^ 2 – 2gx – 2fy g ^ 2 f ^ 2 – r = 0 Deje g ^ 2 f ^ 2 – r = c entonces tenemos x ^ 2 y ^ 2 – 2gx – 2fy c = 0 En algunas convenciones, tomamos el centro del círculo como (g, f) Eso explica el signo positivo en la ecuación
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If the circle x^2y^22gx2fyc=0 is touched by y=x at P such that O P=6sqrt(2), then the value of c is 36 (b) 144 (c) 72 (d) none of these Apne doubts clear karein ab Whatsapp par bhi Try it now CLICK HERE 1x 15x 2x Loading DoubtNut Solution for you Let S ≡ x 2 y 2 2gx 2fy c = 0 be a given circle Find the locus of the foot of the perpendicular drawn from the origin upon any chord of S which subtends a right angle at the origin 👍 Correct answer to the question If x^2y^22gx2fyc=0 is equation of smallest circle is passing through (1,2) and touches line xy7=0 then value of (g2f3c) is eanswersin
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Stepbystep explanation We know General equation of second degree ax^2 by^2 2hxy 2gx2fyc =0 (1) , represents a circle when h= 0 & a=b And when a=b=1, then the above equation (1) becomes x^2y^22gx2fyc=0, (2), if we add g^2 & f^2 on both the side of equation (2) , we get x^2 2gx g^2 y^22fyf^2 = g^2f^2cThe equation x^(2) y^(2) 2gx 2fy c = 0 represents a circle of nonzero radius , if Apne doubts clear karein ab Whatsapp par bhi Try it nowThe general solution of the differential equation of all circles having centre at A( 1, 2) is x 2 y 2 2x 4y c = 0 Explanation General equation of a circle with centre ( g, f) is x 2 y 2 2gx 2fy c = 0 If ( g, f) = A ( 1, 2) Then equation of circle, x 2 y 2 2x 4y c = 0
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To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW Solve the differential equation `(x^2y^2)dx2xydy=0`Click here👆to get an answer to your question ️ Let x^2 y^2 2gx 2fy c = 0 be equation if circle touches positive x axis and intersect y axisGiven equation of a pair of straight lines is x 2 y 2 2gx 2fy 1 = 0 Comparing with the general equation, ax 2 by 2 2hxy 2gx 2fy c = 0, We get a = 1, b = 1, h = 0, g = g, f = f, c = 1 The condition for pair of straight lines is
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To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW The length of the shortest chord of the circles `x^2 y^22gx 2fyc=0 ` whichThe general equation of conics of a second degree is given by \(a{x^2} 2hxy b{y^2} 2gx 2fy c = 0\) and discriminant Δ = abc 2fgh – af 2 – bg 2 – ch 2 The above given equation represents a nondegenerate conics whose nature is given below in the tableA General Equation Of Second Degree Ax2 2hxy By2 2gx 2fy C 0 Represents A Pair Of Straight Lines If A general equation of second degree ax 2 2hxy by 2 2gx 2fy c = 0 represents a pair of straight lines if 1) is confocal with the ellipse 3x 2 y 2 = 12 then, its equation is
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