Question

PSQ is a focal chord of the parabola y2=16x .if p=(1,4) then SP÷SQ

Answer 1

Given : PSQ is a focal chord of the parabola, y² = 16x. point P = (1, 4)

To find : find the value of SP/SQ

solution : concept : if PSQ is a focal chord of parabola y² = 4ax (a > 0), where S is focus then

1/SP + 1/SQ = 1/a

here, y² = 16x = 4(4)x

on comparing with y² = 4ax, we get a = 4

so, 1/SP + 1/SQ = 1/4 .........(1)

focus point of y² = 4ax is (a, 0)

so, focus of y² = 16x is (4, 0)

so length of SP = √{(4 - 1)² + (4 - 0)²}

= √{3² + 4²} = 5 , putting this in equation (1) we get,

1/5 + 1/SQ = 1/4

⇒1/SQ = 1/4 - 1/5 = 1/20

⇒SQ = 20

therefore SP/SQ = 5/20 = 1/4