Question

Find the co-ordinates of the focus, axis of the parabola, the equation of the directrix and the length of latus rectum of teh parabola $y^2=-8x$.

Answer 1

From the question we can get,

Equation of the parabola $y^2=-4ax$

Since the coefficient of x is negative the curve is open towards left.

Coordinates of focus is (-a, 0)

Length of the latus rectum is 4a.

Equation of directrix is x-a = 0

The given equation is $y^2=-8x$

Comparing this equation with $y^2=-4ax$

$4a=8$

$a=2$

Hence the coordinates of focus are (-2,0)

Since the given equation involves $y^2,$ the axis of the parabola is x-axis.

Axis : x-axis

Equation of the directrix : $x=a$ i.e.$x=2$

Length of the latus rectum :$4a=4\times 2=8$