List of top Mathematics Questions on Ellipse asked in JEE Main

The acute angle between the pair of tangents drawn to the ellipse 2x2 + 3y2 = 5 from the point (1, 3) is

The locus of the mid-point of the line segment joining the point (4, 3) and the points on the ellipse x2 + 2y2 = 4 is an ellipse with eccentricity:

If m is the slope of a common tangent to the curves
\(\frac{x²}{16} + \frac{y²} {9} = 1\)
and x2 + y2 = 12, then 12m2 is equal to:

Let the eccentricity of an ellipse \(\frac {x^2}{a^2}+\frac {y^2}{b^2}=1\), \(a>b\), be \(\frac 14\). If this ellipse passes through the point \((−4\sqrt {\frac 25},3)\), then \(a^2 + b^2\) is equal to :

If the length of the latus rectum of the ellipse x2 + 4y2 + 2x + 8y – λ = 0 is 4, and l is the length of its major axis, then λ + l is equal to ________.
Let a line L pass through the point intersection of the lines \(bx + 10y – 8 = 0\) and \(2x - 3y = 0, \quad b \in \mathbb{R} - \left\{\frac{4}{3}\right\}\). If the line L also passes through the point \((1, 1)\) and touches the circle \(17(x^2 + y^2) = 16\), then the eccentricity of the ellipse \(\frac{x^2}{5} + \frac{y^2}{5} = 1\) is
If the minimum area of the triangle formed by a tangent to the ellipse $\frac{x^2}{b^2} + \frac{y^2}{4a^2} = 1$ and the co-ordinate axis is kab, then k is equal to _________.
Let the ellipse, $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, a > b,$ pass through the point (2, 3) and have eccentricity equal to $\frac{1}{2}$. Then equation of the normal to this ellipse at $(2,3)$ is :
The minimum area of a triangle formed by any tangent to the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$ and the co-ordinate axes is :
Let 'd' be the perpendicular distance from the centre of the ellipse x2a2+y2b2= 1 to the tangent drawn at a point P on the ellipse. If F1 and F are two foci of the ellipse, then (PF1 - PF)2  is equal to;