In the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,the equation of the diameter conjugate to the diameter $y = \frac{b}{a}x$ is:

Let $S$ and $S'$ be the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$ and $P$ be a variable point on the ellipse. The maximum area of the triangle $PSS'$ is ............. square units.

The foci of the ellipse $9x^2 + 25y^2 = 225$ are

An ellipse is drawn such that the diameter of the circle $(x - 1)^2 + y^2 = 1$ is the semi-minor axis and the diameter of the circle $x^2 + (y - 2)^2 = 4$ is the semi-major axis. If the center of the ellipse is at the origin and its axes are the coordinate axes,find the equation of the ellipse.

For an ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ with vertices $A$ and $A'$,a tangent drawn at the point $P$ in the first quadrant meets the $y$-axis at $Q$,and the chord $A'P$ meets the $y$-axis at $M$. If $O$ is the origin,then $OQ^2 - MQ^2$ is equal to:

The centre of the ellipse $\frac{(x + y - 2)^2}{9} + \frac{(x - y)^2}{16} = 1$ is