Tag: ellipse

The eccentricity of the ellipse $4x^{2}+16y^{2}=576$ is

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

For all admissible values of the parameter $a$ the straight line $2ax+y\sqrt{1-a^2}=1$ will touch an ellipse whose eccentricity is equal to

If  $( 5,12 )$  and  $( 24,7 )$  are the focii of a conic passing through the origin, then the eccentricity of conic is -

If the focal chord of the ellipse  $\dfrac { x ^ { 2 } } { a ^ { 2 } } + \dfrac { y ^ { 2 } } { b ^ { 2 } } = 1 , ( a > b )$  is normal at  $( a \cos \theta , b \sin \theta )$  then eccentricity of the ellipse is (it is given that  $sin\theta \neq0)$

The eccentricity of the ellipse $\dfrac {x^{2}}{a^{2}} + \dfrac {y^{2}}{b^{2}} = 1$ if its latus-rectum is equal to one half of its minor axis, is

if the distance between the foci is equal to the length of the latus-rectum. Find the eccentricity of the ellipse.

Find the eccentricity of the conic represented by $x^2\, -\, y^2\,- \, 4x\, +\, 4y\, +\, 16\, =\, 0$

If $e _{1}$ is the eccentricity of the ellipse $\displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{25}=1$ and $e _{2}$ is the eccentricity of the hyperbola passing through the foci of the ellipse and $e _{1}e _{2}=1$, then equation of the hyperbola is

What is the eccentricity of the conic $4x^2 + 9 y^2 = 144 $