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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

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The equation of any tangent to y2=4ax is


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





Putting m=−1 in y=mx+am we get,


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

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37. option D (-a, 0), (0, a)

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