Question

Psq is a focal chord of the parabola y^2=16x. If p =(1, 4) then sp /sq=

Answer 1

Given info : psq is a focal chord of the parabola, y² = 16x

To find : if point p = (1, 4) then sp/sq = ?

Solution : focus of parabola (y² = 16x) is (4, 0)

i.e., s = (4,0)

Then, sp = √{(4 - 1)² + (4 - 0)²} = 5

Now using application, 1/sp + 1/sq = 1/a

for y² = 16x = 4(4)x , a = 4

Now, 1/5 + 1/sq = 1/4

⇒1/sq = 1/4 -1/5 = 1/20

⇒sq = 20

Now sp/sq = 5/20 = 1/4

Therefore the value of sp/sq = 1/4

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