Question

If the vertex and the focus of a parabola are $(-1,1)$ and $(2,3)$ respectively, then the equation of the directrix is

• A. $3x+2y+14=0$
• B. $3x+2y-25=0$
• C. $2x-3y+10=0$
• D. none of these

Answer 1

The correct option is A $3x+2y+14=0$

slope of axis $=\frac{3-1}{2+1}=\frac{2}{3}$
Slope of directrix $=\frac{-3}{2}$
Vertex is midpoint of foot of directrix and focus thus we get the coordinates oif foot of directrix as $(-4,-1)$
Equation of directrix will be $\frac{-3}{2}$ $=\frac{y+1}{x+4}$
Option A