Question

The point of intersection of two tangents at the ends of the latus rectum to the parabola $(y+3{)}^2=8(x-2)$ is

• A. $(0,-4)$
• B. $(0,-3)$
• C. $(-1,-3)$
• D. $(-2,-3)$

Answer 1

The correct option is B $(0,-3)$

The tangents at the end points of the latus retum will meet at the point of intersection of axis and directrix
For given parabola $(y+3{)}^2=8(x-2)$
Equation of directrix is $x=0$
Axis of symmetry is $y=-3$
$\therefore$ Tangents meets at $(0,-3)$