Q. 245.0( 1 Vote )

# Equation of the circle through origin which cuts intercepts of length a and b on axes isA. x2 + y2 + ax + by = 0B. x2 + y2 - ax - by = 0C. x2 + y2 + bx + ay = 0D. none of these

Given that we need to find the equation of the circle passing through origin and cuts off intercepts a and b from x and y - axes.

Since the circle is having intercept a from x - axis the circle must pass through (a,0) and (- a,0) as it already passes through the origin.

Since the circle is having intercept b from x - axis the circle must pass through (0,b) and (0, - b) as it already passes through the origin.

Let us assume the circle passing through the points O(0,0), A(a,0) and B(0,b).

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

x2 + y2 + 2fx + 2gy + c = 0 ..... (1)

Substituting O(0,0) in (1), we get,

02 + 02 + 2f(0) + 2g(0) + c = 0

c = 0 ..... (2)

Substituting A(a,0) in (1), we get,

a2 + 02 + 2f(a) + 2g(0) + c = 0

a2 + 2fa + c = 0 ..... (3)

Substituting B(0,b) in (1), we get,

02 + b2 + 2f(0) + 2g(b) + c = 0

b2 + 2gb + c = 0 ..... (4)

On solving (2), (3) and (4) we get,

Substituting these values in (1), we get

x2 + y2 - ax - by = 0

Similarly, we get the equation x2 + y2 + ax + by = 0 for the circle passing through the points (0,0), (- a,0), (0, - b).

The equations of the circles are x2 + y2±ax±by = 0.

The correct options are (a) and (b).

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 circles56 mins
Lecture on radical axis of 2 circlesFREE Class
Lecture on Tangents to a Circle57 mins
General & parametric form of circle56 mins
Practice Problems on Equation of Circle54 mins
Family of circlesFREE Class
Locus involving circles45 mins
Standard Equation of CircleFREE Class
Interactive Quiz on Common tangents & angle of intersection of 2 circlesFREE Class
Quiz 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
view all courses