Question

Find the length of focal chord of the parabola `x^(2)=4y` which touches the hyperbola `x^(2)-4y^(2)=1` _________

Answer 1

Correct Answer - 9
Let point `(2t_(1),t_(1)^(2)` and `(2t_(2),t_(2)^(2))` be the extremities of focal chord
`implies t_(1)t_(2)=-1`
Equation of focal chord `x(t_(1)+t_(2))-2y+2=0` and line `=mx+sqrt(m^(2)-1/4)` is tangent to hyperbola passes through `(0,a)`
`impliesm=+-sqrt(1+1/4)=t_(1)+t_(2)`
Length of focal chord `=9`