The number of points which can be expressed in the form $(p_1/q_1, p_2/q_2)$,where $p_i$ and $q_i$ $(i = 1, 2)$ are co-primes,and lie on the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ is:

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(\pm 3, 0)$,ends of minor axis $(0, \pm 2)$.

Find the coordinates of the foci,the vertices,the length of the major axis,the minor axis,the eccentricity,and the length of the latus rectum of the ellipse $36 x^{2}+4 y^{2}=144$.

If $S$ and $S^{\prime}$ are the foci of the ellipse $\frac{x^2}{18}+\frac{y^2}{9}=1$ and $P$ is a point on the ellipse,then $\min \left(SP \cdot S^{\prime}P\right) + \max \left(SP \cdot S^{\prime}P\right)$ is equal to:

The ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ and the straight line $y = mx + c$ intersect in real points only if

The length of the latus rectum of $16x^2 + 25y^2 = 400$ is