Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The centre of a circle passing through the points (0, 0), (1, 0) touching the circle x 2 + y 2 = 9 is -
Text Solution
Verified by ExpertsThe correct answer is:
D
C 1 = x 2 + y 2 – 9 = 0 ; C 2 = x 2 + y 2 + 2gx + 2fg + c = 0
passes (0,0) ⇒ c = 0
⇒ passes (1, 0) ⇒ 1 + 2g = 0 ⇒ g = –1/2
C 2 (–g, –f) ; (r 2 = 
)
C 2 (1/2, –f) ; r 2 = 
touches internally
C 1 C 2 = |r 1 – r 2 |
= 3 – 
2 
= 3 ⇒ 4(1/4 + f 2 ) = 9 ⇒ f = ± 
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
A point P moves in such a way that the ratio of its distances from two coplanar points is always fi…
The equation of a circle with origin as centre passing through the vertices of an equilateral trian…
If the line is a diameter of the circle then b =
The centre of the circle is
Let be the equation of a circle. If has equal roots and has roots then the centre of the circl…
If the lines and are tangents to a circle, then the radius of the circle is