Let P(6,3) be a point on the hyperbola x^2 a^2 - y^2 b^2 =1 . If the normal at the point P intersects the X -axis at (9,0) , then the eccentricity of the hyperbola is

Step-by-step solution

Equation of normal to hyperbola at (x₁, y₁ ) is gathered a^2 x x₁ + b^2 y y₁ =a^2+b^2 At (6,3), a^2 x 6 + b^2 y 3 =a^2+b^2 gathered It passes throught (9,0) . aligned & Now, a^2 9 6 =a^2+b^2 & 3 a^2 2 -a^2=b^2 a^2 b^2 =2 & e^2=1+ b^2 a^2 =1+ 1 2 e= 3 2 aligned