Question

find coordinates of point on parabola y² = 32x having focal distance 10  

Answer 1

STEP 1 : 

Equation of parabola : y² = 32x

On comparing with : y² = 4ax , 4a = 32 , a = 8 

STEP 2 : 

Focal distance of point P(x,y) = 10 

PS = 10 

PM = 10 ……….. FOCUS DIRECTRIX PROPERTY 

x + a = 10 

x + 8 = 10 

x = 2 

STEP 3 : 

P(2 , y) lies on parabola y² = 32x & hence it must satisfy the equation of parabola 

∴ y² = 16(2) 

y² = 64 , 

y = ± 8 

∴ P(2,8) & P’(2,–8)