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36. The equation of common tangent to y2 = 4ax and x2=4ay is
37. Parabola P always passes through the points

2 Answers

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Best answer

36.

The equation of any tangent to y2=4ax is

y=mx+ma​

If it touches x2=4ay then, the equation.

⇒x2=4a(mx+ma​) has equal roots.

⇒mx2−4am2x−4a2=0 has equal roots

If the roots are equal, the discriminant is equal to 0

i.e.,b2−4ac=0

⇒16a2m4+16a2m=0

⇒16a2m4=−16a2m

m=−1

Putting m=−1 in y=mx+am we get,

y=−x−a

⇒x+y+a=0 This is the common tangent to the two parabola.

+2 votes
by (284 points)
37. option D (-a, 0), (0, a)

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