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JEE Advanced Mathematics question

MathematicsParabolaJEE Advanced

Let PQ be a chord of the parabola . A circle drawn with PQ as a diameter passes through the vertex V of the parabola. If arPVQ unit then the coordinates of P are

Answer: (A),(B)

Solution

Since V lies on the circle with diameter PQ, .

*(Figure: parabola with vertex V(0,0); P on the upper branch, Q on the lower branch; VP ⟂ VQ.)*

Let . Slope of VP , so VQ is . Solving with :

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Question ID VK-109045