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find coordinates of point on parabola y2 = 4x having focal distance 5

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STEP 1 : 

Equation of parabola : y2 = 4x 

On comparing with : y2 = 4ax , 4a = 4 , a = 1

STEP 2 : 

Focal distance of point P(x,y) = 5 

PS = 5 

PM = 5 ……….. FOCUS DIRECTRIX PROPERTY 

x + a = 5 

x + 1 = 5 

x = 4

STEP 3 : 

P(4 , y) lies on parabola y2 = 4x & hence it must satisfy the equation of parabola 

 y2 = 4(4) 

y2 = 16 , ` 

y = ± 4 

 P(4,4) & P’(4,-4)

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