Question

Find coordinates of focus ; equation of directrix ; length of latus rectum and ends of latus rectum

y² = 12x

Answer 1

Equation of parabola : y² = 12x

On comparing with : y² = 4ax , 4a = 12 , a = 3

Focus : S = (a,0) = (3,0) 

Equation of directrix : 

x + a = 0 

∴ x + 3 = 0 

Length of latus recturm = 4a = 12 units 

Ends of latus rectum : L = (a , 2a) = (3,6) 

L’ = (a,-2a) = (3,-6)