Question

2.
If (0, 0) be the vertex and 3x - 4y + 2 = 0 be the
directrix of a parabola, then the length of its latus
rectum is-
(1) 4/5 (2) 2/5 (3) 8/5 (4) 1/5​

Answer 1

Length of latus rectum is $\frac{8}{5}$

Explanation:

Given: If $(0,0)$ be the vertex and $3x-4y+2=0$ be the

directrix of a parabola.

To find: The length of its latus  rectum

Solution:

We know that the distance between the directrix and the focus is

$d=\left | \frac{Ax_{1}+By_{1}+C}{\sqrt{^{A^{2}+B^{2}}}}\right |$

Here, $A=3$, $B=-4$, $x_{1} =0$ and $y_{1} =0$

So, we have

$d=\left | \frac{3\times0+(-4)\times0+2}{\sqrt{^{3^{2}+(-4)^{2}}}}\right |$

$d=\left | \frac{2}{\sqrt{25}}}}\right |$

$d=\frac{2}{5}$

So, we get $a=\frac{2}{5}$

Now, we know that length of latus rectum is 4a.

Therefore, length of latus rectum is $4\times\frac{2}{5}=\frac{8}{5}$

Learn more:

The focus of a parabola is (1,5) and ita directrix is the straight line x+y+2=0

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