Question

The equation of the directrix of the parabola whose vertex (3, 2) and focus (2, –1) is

• A. x + 3y – 19 = 0
• B. y - 2y – 9 = 0
• C. 2x + 6y – 24 = 0
• D. x – 3y – 19 = 0

Answer 1

The correct option is A x + 3y – 19 = 0

A (3, 2) S (2, –1). Let Z be the projection of S on the directrix
Now A is the mid point of $\overline{SZ}\therefore Z(2\times 3-2,2\times 2+1)=(4,5)$
Slope of $\overleftrightarrow{SZ}is\frac{5+1}{4-2}=3\Rightarrow$ Slope of the directrix is $-\frac{1}{3}$
$\therefore$ Equation of he directrix is x + 3y – 19 = 0
Note: Focus, vertex and foot of perpendicular of vertex on directrix lie on line and vertex is the midpoint of the other two. Directrix is perpendicular to the line joining these three points.