The locus of the point which is such that the chord of contact of tangents drawn from it to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` forms a triangle of constant area with the coordinate axes is (a) straight line (b) a hyperbola (c) an ellipse (d) a circle

Options

A. a straight line
B. a hyperbola
C. an ellipse
D. a circle

Answer

B

Explanation

The chord of contact of tangents from `(x_(1),y_(1))` is
`(x x_(1))/(a^(2))+(yy_(1))/(b^(2))=1`
It meets the axes at the points `(a^(2)//x_(1),0) and (0, b^(2)//y_(1))`.
Area of triangle `=(1)/(2)(a^(2))/(x_(1))(b^(2))/(y_(1))=k("constant")`
`"or "x_(1)y_(1)=(a^(2)b^(2))/(2k)=c^(2)" (c is constant)"`
Therefore, `xy=c^(2)` is the required locus.