Question:
Let \(S\) be the focus of the parabola \(y^2=8x\) and \(PQ\) be the common chord of the circle \(x^2+y^2-2x-4y=0\) and the given parabola. The area of \(\triangle PQS\) is
Let \(S\) be the focus of the parabola \(y^2=8x\) and \(PQ\) be the common chord of the circle \(x^2+y^2-2x-4y=0\) and the given parabola. The area of \(\triangle PQS\) is
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Use focus–chord area property.
Updated On: Mar 23, 2026
- \(4\) sq units
- \(3\) sq units
- \(2\) sq units
- \(8\) sq units
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Focus of \(y^2=8x\) is \((2,0)\).
Step 2: Common chord obtained by subtracting equations: \[ y^2-8x-(x^2+y^2-2x-4y)=0 \Rightarrow x^2-6x+4y=0 \]
Step 3: Area of triangle with focus gives \(4\).
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