Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The circles 
and 
intersect in two distinct points 
and 
, then find the number of values of ' 
' for which the line 
by 
passes through 
and Q .
Text Solution
Verified by ExpertsThe correct answer is:
0
(0)
Sol. Let S 1 : x 2 + y 2 + 2ax + cy + a = 0
S 1 : x 2 + y 2 – 3ax + dy – 1 = 0
common chord S 1 – S 2 = 0 ⇒ 5ax + y(c – d) + (a + 1) = 0
given line is 5x + by – a = 0
compare both 
= 
= 
⇒ a = 
= –1 – 
(i) (ii) (iii)
From (i) & (iii) a 2 + a + 1 = 0 ⇒ a = ω , ω 2 no real a.
──────────────────────────────────────────────────────────────────────────────────────────
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
Column – I Column – II
[16JM110516]
If , , & are four distinct points on a circle of radius 4 units, then abcd is equal to:
From the point A (0 , 3) on the circle x² + 4x + (y − 3)² = 0 a chord AB is drawn & extended to a p…
If tangent at (1, 2) to the circle intersects the circle at and tangents at A & B to the second …
A circle passes through point touches the line pair . Centre of circle lies inside the circle Co…
The length of the tangents from any point on the circle to the two circles and are in the ratio