If vertex of parabola is 2 , - 1 and equation of its directrix is 4 x - 3 y = 21 , then the length of latus rectum is

Question

Aicharya · Accepted Answer

Plotting the graph with given data we have,

We know that, in any parabola, the length of the latus rectum $= 4 a$ and perpendicular distance from vertex to the directrix $= a$

So, $a = |\frac{8 + 3 - 21}{\sqrt{4^{2} + {(- 3)}^{2}}}|$

$\Rightarrow a = |\frac{- 10}{5}| = 2$

Therefore, the length of the latus rectum $4 a = 4 \times 2 = 8$

If vertex of parabola is 2 , - 1 and equation of its directrix is 4 x - 3 y = 21 , then the length of latus…