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Most Important Selected Qs for JEE AdvancedMathematicsHyperbola

A hyperbola has the equation x^2 a^2 - y^2 b^2 =1 . A tangent and normal to the hyperbola is drawn at the same point. The tangent has y -intercept and normal has y -intercept . If =-4 and =9 then find the x coordinate of the focus c of hyperbola. (Given c lies on the positive x -axis.)

Correct answer

6

Step-by-step solution

aligned & T : x a - y b =1 & x=0 y=-b =-4 aligned b =4 ....(1) N : a x + b y =a^2+b^2x=0 ; y= a^2+b^2 b =9 ...(2) Eqn. (1) Eqn. (2) aligned a^2+b^2 & =36=a^2 e^2 a e & = 6 aligned x -coordinate of c is a e=6

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