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Maths Conic Sections Hyperbola Single Correct MCQ
Published on: August 13, 2026

The condition that straight line with slope m will be normal to the parabola y 2 = 4ax as well as a tangent to the rectangular hyperbola x 2 - y 2 = a 2 is

A
m 6 - 4m 2 + 2m - 1 = 0
B
m 4 + 3m 3 +2m + 1 = 0
C
m 6 - 2m = 0
D
m 6 + 4m 4 + 3m 2 + 1 = 0

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Verified by Experts
The correct answer is:
D

The equation of normal to the parabola y = mx – 2am – am 3 if ‘m’ in the slope of the normal if it is a tangent to the hyperbola x 2 – y 2 =a 2 then

(-2am – am 3 ) 2 = a 2 m 2 - a 2

(2m+m 3 ) 2 = m 2 – 1

m 6 + 4m 4 + 4m 2 = m 2 – 1

m 6 + 4m 4 + 3m 2 + 1 = 0.

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