Consider the chords of the parabola `y^(2)=4x` which touches the hyperbola `x^(2)-y^(2)=1`, the locus of the point of intersection of tangents drawn to the parabola at the extremitites of such chords is a conic section having latursrectum `lambda`, the value of `lambda`, is

Options

A. `1`
B. `2`
C. `3`
D. `4`

Explanation

Let `P(h,k)` be the point of intersection of the tangents to the parabola at the end-points of the chord. Then, the chord is the chord of contact of tangents drawn from the point `(h,k)` and its equation is
`ky=2(x+h)` or, `y=(2k)/(k)+(2h)/(k)`
It touches the hyperbola `x^(2)-y^(2)=1`.
`:.((2h)/(k))^(2)=((2)/(k))^(2)-1` or, `4h^(2)+k^(2)=4`
Hence, the locus of `(h,k)` is `4x^(2)+y^(2)=4`, which is an ellipse of of latursrecturm `1`.