Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let S be the focus of the parabola y 2 = 8x and let PQ be the common chord of the circle x 2 + y 2 – 2x – 4y = 0 and the given parabola. The area of the triangle PQS is.
Text Solution
Verified by ExpertsThe correct answer is:
4
(4)
Focus is S ≡ (2, 0). Points P ≡ (0, 0) and Q = (2t 2 , 4t)
Area of PQS = 
= 
(8t) = 4 t ......(i)
Q (2t 2 , 4t) satisfies circle
4t 4 + 16t 2 – 4t 2 – 16t = 0
t 3 + 3t – 4 = 0
(t – 1) (t 2 + t + 4) = 0
put t = 1 in Area of PQS. ⇒ Area of PQS is 4
──────────────────────────────────────────────────────────────────────────────────────────
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
The tangent PT and the normal PN to the parabola y 2 = 4ax at a point P on it meet its axis at poin…
The line passing through the extremity A of the major axis and extremity B of the minor axis of the…
In a triangle ABC with fixed base BC, the vertex A moves such that cos B + cos C = 4 sin 2 . If a,…
The normal at a point P on the ellipse x 2 + 4y 2 = 16 meets the x-axis at Q. If M is the mid point…
Match the conics in Column - I with the statements/expressions in Column - II.
Column - I Column - …
An ellipse intersects the hyperbola 2x 2 – 2y 2 = 1 orthogonally. The eccentricity of the ellipse i…