The locus of the point of intersection of perpendicular tangents to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, is
${x^2} + {y^2} = {a^2} - {b^2}$
${x^2} - {y^2} = {a^2} - {b^2}$
${x^2} + {y^2} = {a^2} + {b^2}$
${x^2} - {y^2} = {a^2} + {b^2}$
The area of the rectangle formed by the perpendiculars from the centre of the standard ellipse to the tangent and normal at its point whose eccentric angle is $\pi /4$ is :
The equation of an ellipse, whose vertices are $(2, -2), (2, 4)$ and eccentricity $\frac{1}{3}$, is
The centre of the ellipse $4{x^2} + 9{y^2} - 16x - 54y + 61 = 0$ is
In an ellipse the distance between its foci is $6$ and its minor axis is $8$. Then its eccentricity is
The equation of ellipse whose distance between the foci is equal to $8$ and distance between the directrix is $18$, is