Q. 15

Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y – 4x + 3 = 0.

Answer :

Given that we need to find the equation of the circle which passes through (2,3), (4,5) and has its centre on the line y - 4x + 3 = 0. ..... (1)



We know that the standard form of the equation of the circle is given by:


x2 + y2 + 2ax + 2by + c = 0 .....(2)


Substituting centre (- a, - b) in (1) we get,


- 4(- a) + (- b) + 3 = 0


4a - b + 3 = 0 ......(3)


Substituting (2,3) in (2), we get


22 + 32 + 2a(2) + 2b(3) + c = 0


4 + 9 + 4a + 6b + c = 0


4a + 6b + c + 13 = 0 ..... (4)


Substituting (4,5) in (2), we get


42 + 52 + 2a(4) + 2b(5) + c = 0


16 + 25 + 8a + 10b + c = 0


8a + 10b + c + 41 = 0 ..... (5)


Solving (3), (4) and (5) we get,


a = - 2,b = - 5,c = 25


Substituting these values in (2), we get


x2 + y2 + 2(- 2)x + 2(- 5)y + 25 = 0


x2 + y2 - 4x - 10y + 25 = 0


The equation of the circle is x2 + y2 - 4x - 10y + 25 = 0.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Lecture on Common tangents & angle of intersection of 2 circlesLecture on Common tangents & angle of intersection of 2 circlesLecture on Common tangents & angle of intersection of 2 circles56 mins
Lecture on radical axis of 2 circlesLecture on radical axis of 2 circlesLecture on radical axis of 2 circles48 mins
Lecture on Tangents to a CircleLecture on Tangents to a CircleLecture on Tangents to a Circle57 mins
General & parametric form of circleGeneral & parametric form of circleGeneral & parametric form of circle56 mins
Practice Problems on Equation of CirclePractice Problems on Equation of CirclePractice Problems on Equation of Circle54 mins
Family of circlesFamily of circlesFamily of circles55 mins
Locus involving circlesLocus involving circlesLocus involving circles45 mins
Interactive quiz on equation of circleInteractive quiz on equation of circleInteractive quiz on equation of circle50 mins
Interactive Quiz on Family of circlesInteractive Quiz on Family of circlesInteractive Quiz on Family of circles58 mins
Quiz on Tangents to a CircleQuiz on Tangents to a CircleQuiz on Tangents to a Circle48 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