Hyperbola Question - None

Question

Equation of tangent to hyperbola \frac{xh}{a^2} - \frac{yk}{b^2} = 1\ at point P(h,k)\ touches the parabola at point (at^2, 2at)\

Accepted Answer

Solution:

Equation of tangent to hyperbola: y = mx \pm \sqrt{a^2m^2 - b^2}\

For the tangent to parabola y^2 = 4ax\, we equate:

a^2m^2 - b^2 = \frac{a^2}{m^2}\

a^2m^4 - b^2m^2 - a^2 = 0\

Solving: m^2 = \frac{b^2 \pm \sqrt{b^4 + 4a^4}}{2a^2}\

∴ Answer is (b)

Question: