Question

Find the equation of the parabola with focus F(4, 0) and directrix x = -4.

Answer 1

Given equation of directrix : x = -4 

• x + 4 = 0 

Above equation is of the form, x + a = 0 

Focus of the parabola F(4,0) is of the form F(a,0) 

Therefore, a = 4 

For directrix with equation x + a=0 and focus (a,0), equation of the parabola is, 

y² = 4ax 

• y² = 16x