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

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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)

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