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Maths Conic Sections Parabola Single Correct MCQ
Published on: August 11, 2026

The two parabolas and intersect at a point P , whose abscissa is not zero, such that

A
They both touch each other at P
B
They cut at right angles at P
C
The tangents to each curve at P make complementary angles with the x -axis
D
None of these

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The correct answer is:
C

Solving and we get and . Therefore the co-ordinates of P are (4,4). The equations of the tangents to the two parabolas at (4,4) are .....(i)

.....(ii)

Now, Slope of (i) Slope of (ii)

∴ ∴ .

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