Q. 133.8( 96 Votes )

Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.

Answer :

Let the equation of the required circle be (x – h)2+ (y – k)2 =r2


Since, the circle passes through (0, 0),


(0 – h)2+ (0 – k)2 =r2


h2 + k2 = r2


The equation of the circle now becomes (x – h)2+ (y – k)2 = h2 + k2.


It is given that the circle makes intercepts a and b on the coordinate axes.


That means that the circle passes through points (a, 0) and (0,b). Therefore,


(a – h)2+ (0 – k)2 =h2 +k2.................(1)


(0 – h)2+ (b– k)2 =h2 +k2..................(2)


From equation (1), we obtain


a2 – 2ah + h2 +k2 = h2 +k2


a2 – 2ah = 0


a(a – 2h) =0


a = 0 or (a -2h) = 0


However, a 0; hence, (a -2h) = 0

h =.


From equation (2), we obtain


h2  – 2bk + k2 + b2= h2 +k2


b2 – 2bk = 0


b(b– 2k) = 0


b= 0 or (b-2k) =0


However, a 0; hence, (b -2k) = 0

 k =.



+=


4x2 -4ax + a2 +4y2 - 4by + b2 =a2 + b2


4x2 + 4y2 -4ax – 4by =0


4( x2 +y2 -7x + 5y – 14 ) = 0


x2+y2- ax - by=0

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz on properties of focal chord of parabolaQuiz on properties of focal chord of parabolaQuiz on properties of focal chord of parabola36 mins
Properties of tangents to parabolaProperties of tangents to parabolaProperties of tangents to parabola42 mins
Focal chord of parabolaFocal chord of parabolaFocal chord of parabola29 mins
Equation of tangent to parabola | Conic SectionEquation of tangent to parabola | Conic SectionEquation of tangent to parabola | Conic Section38 mins
Equation of tangent to parabola | Conic Section | QuizEquation of tangent to parabola | Conic Section | QuizEquation of tangent to parabola | Conic Section | QuizFREE Class
Interactive Quiz on Equation of ParabolaInteractive Quiz on Equation of ParabolaInteractive Quiz on Equation of Parabola41 mins
Lecture on Equation of ParabolaLecture on Equation of ParabolaLecture on Equation of Parabola59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses