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in Mathematics by (67.9k points)

10 A tangent PT is drawn at the point P(16, 16) to the parabola y2 = 16x. PT tangent intersect the x-axis at T. If S be the focus of the parabola, then ∠TPS is equal to

(a)   tan-11/2

(b)   π/4

(c)   1/2tan-1 1/2

(d)   tan-1 3/4

1 Answer

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Best answer

Correct option  (a)  tan–1 1/2

Explanation:

ST = 4 + AT = 16 + 4 = 20

PS = 4 + 16 = 20

ΔTPS is isosceles triangle

tan 2θ = 16 - 0/16 - 4 = 4/3 = 2 tanθ/1 - tan2θ

2 tan2 θ + 3tan θ – 2 = 0 

(2 tan θ –1) (tan θ + 2) = 0

tan θ = 1/2 , tanθ = –2

θ  = tan–1 1/2

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