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JEE Main202226 Jun 2022Evening ShiftMathematicsHyperbolaActual

Let a line L 1 be tangent to the hyperbola x 2 16 - y 2 4 = 1 and let L 2 be the line passing through the origin and perpendicular to L 1 . If the locus of the point of intersection of L 1 and L 2 is x 2 + y 2 2 = α x 2 + β y 2 , then α + β is equal to ______.

Correct answer

0

Step-by-step solution

The equation of tangent to the given hyperbola is y = m x ± 16 m 2 - 4         . . . i Hence, l 1 : y = m x ± 16 m 2 − 4 Given that, l 2 is a straight line passing through origin and perpendicular to l 1 . So, l 2 : y = - 1 m x ⇒ m = - x y           . . . ii On solving equations i & ii , we get y = - x y x ± 16 - x y 2 - 4 ⇒ y = - x 2 y ± 16 x 2 - 4 y 2 y ⇒ y 2 + x 2 2 = 16 x 2 - 4 y 2 On comparing the above equation with x 2 +

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