The point of intersection of the tangents drawn to the hyperbola x 2 a 2 - y 2 b 2 = 1 at the points where it is intersected by the line l x + m y + n = 0 is

Question

The point of intersection of the tangents drawn to the hyperbola x 2 a 2 - y 2 b 2 = 1 at the points where it is intersected by the line l x + m y + n = 0 is, a 2 l n , b 2 m n, a 2 l n , - b 2 m n, - a 2 l n , b 2 m n, - a 2 l n , - b 2 m n

MARKS App · Accepted Answer

Let, x 1 , y 1 be the required point. Then, the equation of the chord of contact of the tangents drawn from x 1 , y 1 to the given hyperbola is x x 1 a 2 - y y 1 b 2 = 1 …(i) The given line is l x + m y + n = 0 …(ii) Equations (i) and (ii) represent the same line ∴ x 1 a 2 l = - y 1 b 2 m = 1 - n ⇒ x 1 = - a 2 l n , y 1 = b 2 m n . Hence, the required point is - a 2 l n , b 2 m n

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