The point of intersection of the latus rectum and axis of the parabola y 2 + 4 x + 2 y - 8 = 0 is

Question

Aicharya · Accepted Answer

The point of intersection of the latus rectum and axis of the parabola $y^{2} + 4 x + 2 y - 8 = 0$ is the focus of the parabola.

$y^{2} + 4 x + 2 y - 8 = 0$

$\Rightarrow y^{2} + 2 y + 1 = - 4 x + 8 + 1$

$\Rightarrow {(y + 1)}^{2} = 4 (- 1) (x - \frac{9}{4})$

We know that the focus of the parabola ${(y - k)}^{2} = 4 a (x - h)$ is $S \equiv (a + h, k)$ .

So, the focus of the given parabola is $S \equiv (- 1 + \frac{9}{4}, - 1) \equiv (\frac{5}{4}, - 1)$ .

Solution