List of top Mathematics Questions on Ellipse asked in MHT CET

If the line \(4x-3y+k=0\) touches the ellipse \(5x^{2}+9y^{2}=45\), then the value of \(k\) is
The point on the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\) which is equidistant from its foci can be
Tangents are drawn from the point \(P(3,4)\) to the ellipse \(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1\) touching the ellipse at points A and B. Then length of segment AB is
In an ellipse with semi-minor axis OB, S and S' are its foci, \(a>b\) and \(\angle SBS'\) is a right angle, then the eccentricity of the ellipse is..
If \(P\) be any point on the ellipse \(16x^2+25y^2 = 400\) with foci \(S\) and \(S^'\) and area of \(△PSS^'\) is 9 square units, then the abscissa of point \(P\) is...........
If \(θ\) is the eccentric angle of a point on the ellipse \(\frac{x^2}{25}+\frac{y^2}{9} = 1\) such that the distance of the point from the center is \(5\), then \(θ =\).......
The eccentricity of the ellipse represented by the equation \(7x^2+16y^2-14x+64y-377 = 0\) is...
A tangent having slope \(-\frac{1}{2}\) to the ellipse \(3x^2+4y^2 = 12\) intersects the X-axis and Y-axis at the points A and B respectively. if O is the origin, then the area of \(△AOB\) is ...
If the eccentricity of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1,(a > b)\) is \(\frac{2}{3}\) and its focal chord is \(3x+2y-6 = 0\), then the value of \(a^2+b^2\) is...
The equations of the tangents to the ellipse \(\frac{x^2}{16}+\frac{y^2}{9} = 1\) making an inclination of \(30^{\circ}\) with the major axis are
The ellipse \(4x^2+9y^2 = 1\) intersects positive Y-axis at point A. If S and S' are its foci, then the area (in sq. units) of \(\Delta SAS^'\) is _____

The foci of the conic \(25 x^2+16 y^2-150 x=175\) are

The tangent to the ellipse $9x^{2}+16y^{2}=288$ making equal intercepts on the coordinate axes intersects the X-axis and the Y-axis in the points A and B respectively. Then $A(\triangle OAB)=$ (where O is origin)}

The eccentricity of the curve represented by \(x=3(\cos t+\sin t), y=4(\cos t-\sin t)\) is

AOB is the positive quadrant of the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) in which \(\mathrm{OA}=5, \mathrm{OB}=3\). The area between the arc AB and the chord AB of the ellipse in sq. units is

The eccentricity of the ellipse $9x^2 + 5y^2 - 30y = 0$ is
A normal is drawn at a point $P(x, y)$ of a curve $y = f(x)$. The normal meets the $X$ axis at $Q$. $l(PQ) = k \cdot$ (k is a constant) Then equation of the curve through $(0, k)$ is
The eccentricity of the ellipse $9x^2 + 5y^2 - 30y = 0$ is
A normal is drawn at a point $P(x, y)$ of a curve $y = f(x)$. The normal meets the $X$ axis at $Q$. $l(PQ) = k \cdot$ (k is a constant) Then equation of the curve through $(0, k)$ is