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  4. The feet of the perpendicular drawn from focus upon any tangent to the parabola, y=x2-2 x-3 lies on

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Q. The feet of the perpendicular drawn from focus upon any tangent to the parabola, $y=x^2-2 x-3$ lies on

Conic Sections

Solution:

From the property : the feet of the $\perp r$ will lie on the tangent at vertex of the parabola.
$y=(x-1)^2-3-1$
$(x-1)^2=(y+4)$
Tangent at vertex of above parabola is $y+4=0$.