Tag: maths

The accentricity of the ellipse $4x^{2}+9y^{2}+8x+36y+4=0$ is

Eccentricity of the ellipse $5x^{2}+6xy+5y^{2}=8$ is

An ellipse has $OB$ as its semi-minor axis. $F _{1}$ and $F _{2}$ are its foci and angle $F _{1}BF _{2}$ is a right angle. The eccentricity of the ellipse is 

An ellipse having foci $(3,1)$ and $(1,1)$ passes through the point $(1,3)$ ha the eccentricity 

The tangent at any point $P\left(a\cos\theta,b\sin\theta\right)$ on the ellipse $\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1$ meets the auxiliary circle at two points which subtend a right angle at the center ,then eccentricity is 

If S and S' are the foci of an ellipse of major axis of length 10 units and P is any point on the ellipse such that the perimeter of triangle PSS' is 15 units, then the eccentricity of the ellipse is 

If normal at any point P on the ellipse $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1(a>b>0)$ meet the major and minor axes at Q and R respectively so that 3PQ = @PR, then the eccentricity of ellipse is equal to

Find the length of the semi-axes, coordinates of foci, length of latus rectum, eccentricity and equation direction for the ellipse given by the equations :-  (i) $25{ x }^{ 2 }-150x+16{ y }^{ 2 }=175$ (ii) The eccentricity of the ellipse $9{ x }^{ 2 }+4{ y }^{ 2 }30y=0$ is 

If normal to the ellipse $\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1$ at $\left(ae,\dfrac{b^{2}}{a}\right)$ is passing throught $\left(0,-2b\right)$, then $c=$

An ellipse having foci $\left(3,1\right)$ and $\left(1,1\right)$ passes through the point $\left(1,3\right)$ has the eccentricity