Chapter 10, Problem 1RE

In Problems 1-10, identify each equation. If it is a parabola, give its vertex, focus, and directrix; if it is an ellipse, give its center, vertices, and foci: if it is a hyperbola, give its center, vertices, foci, and asymptotes.

$y^2\text{ = }-16x$

To determine

Each equation. If it is a parabola, give its vertex, focus, and directrix; if it is an ellipse, give its center, vertices, and foci; if it is a hyperbola, give its center, vertices, foci, and asymptotes.

Answer to Problem 1RE

Parabola

Vertex: $\left(0,0\right)$

Focus: $\left(-4,0\right)$

Directrix: $x=4$.

Explanation of Solution

Given:

$y²=-16x$

Formula used:

Vertex	Focus	Directrix	Equation
$\left(0,0\right)$	$\left(-a,0\right)$	$x=a$	$y²=-4ax$

Calculation:

The equation $y²=-16x$ is of the form of a parabola whose equation is $y²=-4ax$.

$a\text{ = 4}$

Vertex at origin $\left(0,0\right)$.

Focus: $\left(-a,0\right),\left(-4,0\right)$.

Directrix: $x=-a$, $x\text{ = 4}$.