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

Question

The feet of the perpendicular drawn from focus upon any tangent to the parabola, y=x2-2 x-3 lies on (A) y+4=0 (B) y=0 (C) y=-2 (D) y+1=0

Tardigrade Admin · Accepted Answer

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.

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

$y + 4 = 0$

$y = 0$

$y = - 2$

$y + 1 = 0$

From the property : the feet of the $⊥ r$ 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 $y + 4 = 0$ .

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

y+4=0

y=0

y=−2

y+1=0