If $A = [(x,\,y):{x^2} + {y^2} = 25]$ and $B = [(x,\,y):{x^2} + 9{y^2} = 144]$, then $A \cap B$ contains
One point
Three points
Two points
Four points
The length of the axes of the conic $9{x^2} + 4{y^2} - 6x + 4y + 1 = 0$, are
If end points of latus rectum of an ellipse are vertices of a square, then eccentricity of ellipse will be -
Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(0,\, \pm \sqrt{5})$ ends of minor axis $(±1,\,0)$
The distance of the point $'\theta '$on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ from a focus is
The number of $p$ oints which can be expressed in the form $(p_1/q_ 1 , p_2/q_2)$, ($p_i$ and $q_i$ $(i = 1,2)$ are co-primes) and lie on the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ is