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Tangent at Vertex when (2,3),(3,2) Equidistant from Focus | JEE

JEE Maths question with a full step-by-step solution.

Question
If the points (2,3)(2, 3) and (3,2)(3, 2) on a parabola are equidistant from the focus, then the tangent at the vertex is:
Aparallel to y=xy = x
Bparallel to y=−xy = -xcorrect
Cparallel to the xx-axis
Dparallel to the yy-axis
Solution
Step 1: Points equidistant from the focus are reflections in the axis, so the chord joining them is perpendicular to the axis — and therefore parallel to the tangent at the vertex. Step 2: Slope of the chord 3−22−3=−1\dfrac{3 - 2}{2 - 3} = -1, so the tangent at the vertex is parallel to y=−xy = -x. Correct answer: (2)
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