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
The eccentricity of ellipse whose line joining foci substends an angle of ${90} _{o}$ at an xtremity of minor axis is
If the roots of the equation $x^2 - 4x + 1 = 0$ are the lengths of the semi-major axis and semi-minor axis of an ellipse, then the eccentricity of the ellipse lies between
If $\alpha,\beta$ are the eccentric of the extremities of a focal chord of an ellipse, then eccentricity of the ellipse is
(-4,1) and (6,1) are the vertices of an ellipse. If one of the foci of the ellipse. If one of the foci of the ellipse lies on x -2y = 2 then its eccentricity is
An ellipse whose foci and $(2,4)$ and $(14,9)$ touches the x-axis then the eccentricity of the ellipse is $\dfrac{P}{\sqrt{q}}$ (when p,q an comprise) then the units place of $p+4q$ is