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

Explanation

Normal at (6, 3) to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` is
`(a^(2)x)/(6)+(b^(2)y)/(3)=a^(2)+b^(2)`
It passes through (9,0).
`therefore" "(9a^(2))/(6)=a^(2)+b^(2)`
`rArr" "(b^(2))/(a^(2))=(1)/(2)`
`rArr" "e^(2)-1=(1)/(2)`
`therefore" "e=sqrt((3)/(2))`