Question

The equation of the director circle of the ellipse \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\] is______.

Options

• \[x^2+y^2=a^2\]

• \[x^2+y^2=a^2-b^2\]

• \[x^2+y^2=2a^2\]

• \[x^2+y^2=a^2+b^2\]

Answer 1

The equation of the director circle of the ellipse \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\] is \[x^2+y^2=a^2+b^2\].

Explanation:

The director circle of an ellipse is the locus of points from which the two tangents drawn to the ellipse are perpendicular to each other, and its equation is \[x^2+y^2=a^2+b^2\].