JEE Main2012MathematicsEllipseActual

The normal at (2, 3 2 ) to the ellipse, x^2 16 + y^2 3 =1 touches a parabola, whose equation is

Options

Ay^2=-104 x
By^2=14 x
Cy^2=26 x
Dy^2=-14 x

Correct answer

A. y^2=-104 x

Step-by-step solution

Ellipse is x^2 16 + y^2 3 =1 Now, equation of normal at (2,3 / 2) is aligned & 16 x 2 - 3 y 3 / 2 =16-3 & 8 x-2 y=13 & y=4 x- 13 2 aligned Let y=4 x- 13 2 touches a parabola y^2=4 a x . We know, a straight line y=m x+c touches a parabola y^2=4 a x if a-m c=0 a-(4) (- 13 2 )=0 a=-26 Hence, required equation of parabola is y^2=4(-26) x=-104 x

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