Question

The locus of the point `P(h, k)` for which the line `hx+ky=1` touches the circle `x^(2)+y^(2)=4`, is
A. a circle
B. a parabola
C. an ellipse
D. a hyperbola

Answer 1

Correct Answer - A
If the line `hx+ky=1` touches the circle `x^(2)+y^(2)=4`, then
`|(hxx0+kxx0-1)/(sqrt(h^(2)+k^(2)))|=2 rArr h^(2)+k^(2)=(1)/(4)`
Hence, the locus of (h, k) is `x^(2)+y^(2)=(1)/(4)`, which is a circle.