Coordinate Geometry
Parabola
MMTS_Full_Test_08
Grade 12
Question:
Let $(2,3)$ be the focus of a parabola and $x+y=0$ and $x-y=0$ be its two tangents, then equation of its directrix will be
$2x-3y=0$
$3x+4y=0$
$x+y=5$
$12x-5y+1=0$
Step-by-Step Solution
Key Concept: Foot of perpendicular from focus to tangent lies on tangent at vertex
Reflecting $(2,3)$ in $x+y=0$ gives $(-3,-2)$ and in $x-y=0$ gives $(3,2)$. Directrix passes through these and is $2x-3y=0$.
Correct Answer: 1