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MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections
Problem If α \alpha α P ( x 1 , y 1 ) P(x_1, y_1) P ( x 1 , y 1 ) S ≡ x 2 + y 2 + 2 g x + 2 f y + c = 0 S \equiv x^2 + y^2 + 2gx + 2fy + c = 0 S ≡ x 2 + y 2 + 2 g x + 2 f y + c = 0 cot α = S 1 g 2 + f 2 − c \cot \alpha = \frac{\sqrt{S_1}}{\sqrt{g^2 + f^2 - c}} cot α = g 2 + f 2 − c S 1 cot α 2 = S 1 g 2 + f 2 − c \cot \frac{\alpha}{2} = \frac{\sqrt{S_1}}{\sqrt{g^2 + f^2 - c}} cot 2 α = g 2 + f 2 − c S 1 tan α = 2 g 2 + f 2 − c S 1 \tan \alpha = \frac{2\sqrt{g^2 + f^2 - c}}{\sqrt{S_1}} tan α = S 1 2 g 2 + f 2 − c α = 2 tan − 1 ( g 2 + f 2 − c S 1 ) \alpha = 2 \tan^{-1} \left( \frac{\sqrt{g^2 + f^2 - c}}{\sqrt{S_1}} \right) α = 2 tan − 1 ( S 1 g 2 + f 2 − c ) Browse the problem library