Let A = 0 , 4 and B = 2 cos θ , 2 sin θ , for some 0 θ π 2 . Let P divide the line segment A B in the ratio 2 : 3 internally. The locus of P is

Question

Let A = 0 , 4 and B = 2 cos θ , 2 sin θ , for some 0 θ π 2 . Let P divide the line segment A B in the ratio 2 : 3 internally. The locus of P is, parabola, ellipse, circle, hyperbola

MARKS App · Accepted Answer

By using section formula: m x 2 + n x 1 m + n , m y 2 + n y 1 m + n P 4 cos θ + 0 5 , 4 sin θ + 12 5 → h , k ⇒ cos θ = 5 h 4 , sin θ = 5 k - 12 4 ⇒ cos 2 θ + sin 2 θ = 1 ⇒ 5 h 4 2 + 5 k - 12 4 2 = 1 ⇒ 5 x 2 + 5 y - 12 2 = 16 (This is the equation of circle)

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