List of top Mathematics Questions on Ellipse asked in WBJEE

$AB$ is a variable chord of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. If $AB$ subtends a right angle at the origin $O$, then $\frac{1}{OA^2} + \frac{1}{OB^2}$ equals to

Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on

The points of the ellipse $16x^2 + 9y^2 = 400$ at which the ordinate decreases at the same rate at which the abscissa increases is/are given by

The line $x=2 y$ intersects the ellipse $\frac{x^{2}}{4}+y^{2}=1$ at the points $P$ and $Q$. The equation of the circle with $P Q$ as diameter is

The eccentric angle in the first quadrant of a point on the ellipse $\frac{x^{2}}{10}+\frac{y^{2}}{8}=1$ at a distance $3$ units from the centre of the ellipse is

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is $90^{\circ}$ The eccentricity of the ellipse is

The equation of a circle of radius 1, touching the circles x² + y² - 2|x| = 0 is

Directions: The following question has four choices, out of which one or more are correct. A charged particle having a positive charge q approaches a grounded metallic neutral sphere of radius R with constant speed v, as shown in the figure. Which of the following alternatives is/are correct?

$\sum _{r=0}^{m}n+r{c}_r$ is equal to

If $y=2x^3-2x^2+3x-5$, then for $x=2$ and $\mathrm{\Delta }x=0.1$ value of $\mathrm{\Delta }y$ is: