The locus of a point whose chord of contact with respect to the circle `x^2+y^2=4` is a tangent to the hyperbola `x y=1` is a/an ellipse (b) circle hyperbola (d) parabola

Options

A. ellipse
B. circle
C. hyperbola
D. parabola

Answer

C

Explanation

Let the point be (h, k).
Then the equation of the chord of contact is `hx+ky=4.`
Since `hx+ky=4` is tangent to xy = 1,
`x((4-hx)/(k))=1`
has two equal roots.
Therefore, discriminant of `hx^(2)-4x+k=0` is 0.
`therefore" "hk=4`
Thus, the locus of (h, k) is xy = 4.