Ellipse · Mathematics · WB JEE

If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the ellipse is

The equation of the ellipse having vertices at ($$\pm$$ 5, 0) and foci ($$\pm$$ 4, 0) is

The latus rectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is

The total number of tangents through the point (3, 5) that can be drawn to the ellipse 3x² + 5y² = 32 and 25x² + 9y² = 450 is

The line y = 2t² intersects the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ in real point if

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

S and T are the foci of an ellipse and B is an end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is

The length of the latus rectum of the ellipse is 16x² + 25y² = 400 is

The equation 8x² + 12y² $$-$$ 4x + 4y $$-$$ 1 = 0 represents

The equation $$\mathrm{r} \cos \theta=2 \mathrm{a} \sin ^2 \theta$$ represents the curve

A line of fixed length $$\mathrm{a}+\mathrm{b} . \mathrm{a} \neq \mathrm{b}$$ moves so that its ends are always on two fixed perpendicular straight lines. The locus of a point which divides the line into two parts of length a and b is

With origin as a focus and $$x=4$$ as corresponding directrix, a family of ellipse are drawn. Then the locus of an end of minor axis is

The tangent at point $$(a\cos \theta ,b\sin \theta ),0 < \theta < {\pi \over 2}$$, to the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ meets the x-axis at T and y-axis at T$$_1$$. Then the value of $$\mathop {\min }\limits_{0 < \theta < {\pi \over 2}} (OT)(O{T_1})$$ is

If the lines joining the focii of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ where $$a > b$$, and an extremity of its minor axis is inclined at an angle 60$$^\circ$$, then the eccentricity of the ellipse is

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

Let f be a strictly decreasing function defined on R such that $$f(x) > 0,\forall x \in R$$. Let $${{{x^2}} \over {f({a^2} + 5a + 3)}} + {{{y^2}} \over {f(a + 15)}} = 1$$ be an ellipse with major axis along the y-axis. The value of 'a' can lie in the interval (s)

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