The area of triangle formed by the tangent and the normal to the parabola y^2=4ax both drawn at the same end of the Latus rectum and the axis of the parabola is

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Saurabh Koranglekar · Answer

Dear student

The line x+y=1 touches the parabola y^2=kx or y^2=4.k/4 x ( Compare with standard eqn y^2=4ax) so a= k/4 and the condition of tangency for the line y=mx+c to a parabola y^2=4ax is that: c=a/m
we gave given c=1, m=-1, a=k/4 This implies 1=k/4(-1) => k=-4

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The area of triangle formed by the tangent and the normal to the parabola y^2=4ax both drawn at the same end of the Latus rectum and the axis of the parabola is

The area of triangle formed by the tangent and the normal to the parabola y^2=4ax both drawn at the same end of the Latus rectum and the axis of the parabola is

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