Question

The equation of locus of a point, the tangents from which to the circle 2x² + 2y² = 18 are at a right angle, is ______ 

Options

• x² + y² = 18 

• x² + y² = 9

• x² + y² = 36

• x² + y² = 27

Answer 1

The equation of locus of a point, the tangents from which to the circle 2x² + 2y² = 18 are at a right angle, is x² + y² = 18.

Explanation:

The locus of the point of intersection of two perpendicular tangents is the director circle.

The equation of the director circle of the circle 

`x^2 + y^2 = a^2` is `x^2 + y^2 = 2a^2`

Equation of circle is x² + y² = 9

Equation of director circle is x² + y² = 2(9)

i.e. x² + y² = 18