Question

Let $AB$ be the focal chord of a parabola $y=x^2-2x+2$ with point $A\equiv (3,5)$ . Then the slope of normal at point $B$ would be :

• A. $\frac{2}{3}$
• B. $6$
• C. $4$
• D. $-0.25$

Answer 1

The correct option is C $4$

Equation of tangent of the given parabola = $\frac{dy}{dx}{|}_{(3,5)}=4$
Let the point of intersection of the tangents and normals at the extremities of the focal chord $AB$ be $P$ and $Q$ respectively.
$\Rightarrow P$ lies on the directrix
and the angle $\angle APB={90}^{\circ }$
So $APBQ$ will be a rectangle.
$\Rightarrow$ Slope of $AP=$
Slope of $BQ=4$