Question

If the vertex of a parabola is $(4,3)$ and its directix is $3x+2y-7=0$ then the equation of latus rectrum of the parabola is

• A. $3x+2y-18=0$
• B. $3x+2y-29=0$
• C. $3x+2y-8=0$
• D. $3x+2y-31=0$

Answer 1

The correct option is B $3x+2y-29=0$

Directrix of parabola $-3x+2y-7=0$

vertex of parabola $-(4,3)$

Latusrectum is parallel to directrix passing from focus.

Slope of latus reactum $=\frac{-3}{2}$

Distance between vertex $=\frac{1}{2}$ (Distance between latus rectum and directrix )

Let equation of latus reactum be $y=\frac{-3}{2}x+c$

$\frac{12+6-7}{\sqrt{3^2+2^2}}=\frac{1}{2}\left(\frac{|\frac{7}{2}-c|}{\sqrt{1+{\left(\frac{-3}{2}\right)}^2}}\right)$

$22=|7-2c|$

$2c-7==22\to 2c>7$

$2c=29$

$c=\frac{29}{2}$

Equation $y=\frac{-3}{2}x+\frac{29}{2}$