List of top Mathematics Questions on Ellipse asked in MET

Condition for line \(lx + my + n = 0\) to be a normal to \(\frac{x^2}{25} + \frac{y^2}{9} = 1\):

The locus of the extremities of the latus rectum of the family of ellipses \(b^2x^2 + y^2 = a^2b^2\) having a given major axis is

Tangent to the ellipse \(\frac{x^2}{32} + \frac{y^2}{18} = 1\) having slope \(-\frac{3}{4}\) meet the coordinate axis at A and B. Then, the area of \(\triangle AOB\), where O is the origin, is

3 numbers are in GP therefore, their logarithms are in

Coefficient of \(x\) in \(f(x) = \begin{vmatrix} x & (1 + \sin x)^3 & \cos x \\ 1 & \log(1 + x) & 2 \\ x^2 & (1 + x)^2 & 0 \end{vmatrix}\) is

The equation of the ellipse whose axes are parallel to the coordinate axes having its centre at the point \( (2, -3) \) and focus at \( (3, -3) \) and one vertex at \( (4, -3) \) is

The angle of intersection of ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) and circle \( x^2 + y^2 = ab \) is:

The number of real tangents that can be drawn to the ellipse $3x²+5y²=32$ passing through (3, 5) is

The center of the ellipse \( \frac{(x+1)^{2}}{9} + \frac{(y-2)^{2}}{4} = 1 \) is:

If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is

The eccentricity of the ellipse \( 9x^{2} + 5y^{2} = 45 \) is:

The center of the ellipse \( \frac{(x+1)^2}{9} + \frac{(y-2)^2}{4} = 1 \) is: