Question

7.Focus (6,0); directrix x =-6

Answer 1

The given focus of parabola is ( 6,0 ) and equation of directrix is

x=−6 (1)

Since the focus lies on the x axis, the equation of the parabola is either y 2 =4ax or y 2 =−4ax

Also, the directrix, x=−6 is to the left the y axis, while the focus (6,0) is to the right of the y axis. Hence, the parabola is of the form y 2 =4ax

Coordinates of focus are given by

( a,0 ) (2)

Equation of directrix is given by

x=−a (3)

By comparing equation (1),(2) and (3) ,we get a=6 .

Equation of parabola is y 2 =4×6×x =24x

Thus, the equation of the parabola with focus (6,0) and equation of directrix x=−6 is y 2 =24x .