Eccentricity of the conic $3x^{2}+2xy-3y^{2}+x+y-2=0$

If circle whose diameter is major axis of ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$ meets minor axis at point P and orthocentre of $\Delta PF _{1}F _{2}$ lies on ellipse where $F _{1}$  and $F _{2}$ are foci of ellipse, then square of eccentricity of ellipse, is 

If (3,4), (5,12) are two foci of the ellipse passing thrpsough the origin. Then the eccentricity of the ellipse is 

An ellipse has foci (3, 1), (1, 1) and it passes through point (1, 3). Its eccentricity is equal to 

The ellipse $E _1:\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$ is inscribed in a rectangle R whose sides are parallel to the coordinates axis. Another ellipse $E _2$ passing through the point $(0, 4)$ circumscribes the rectangle R. The eccentricity of the ellipse $E _2$ is?

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

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 

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 $

If the distance of one of the focus of hyperbola from the two directrices of hyperbola are 5 and 3, then its eccentricity is

The eccentricity of the conic represented by $\sqrt{(x+2)^2+y^2}+\sqrt{(x-2)^2+y^2}=8$ is?

The parabola $( y + 1 ) ^ { 2 } = a ( x - 2 )$ passes through the point $( 1 , - 2 )$ then the equation of its directrix is

The eccentricity of the conic represented by the equation $x^{2} + 2y^{2} - 2x + 3y + 2 = 0$ is

The eccentricity of the conic $9{ x }^{ 2 }+5{ y }^{ 2 }-54x-40y+116=0$ is: