Tag: mathematics and statistics

The equation $\dfrac {x^{2}}{2-r}+\dfrac {y^{2}}{r-5}+1=0$ represents an ellipse, if

The locus of center of a variable circle touching the circle of radius ${ r } _{ 1 }and{ r } _{ 2 }$ extemally which also touch each other externally , is a conic of the eccentricity $e$.If $\dfrac { { r } _{ 1 } }{ { r } _{ 2 } } =3+2\sqrt { 2 } $ then ${ e }^{ 2 }$ is 

The arrangement of the following conics in the descending order of their lengths of semi latus rectum is
A) $ 6= r (1 + 3\cos \theta )$
B) $10= r (1 + 3\cos \theta )$
C) $8= r (1 + 3\cos \theta )$
D) $12= r (1 + 3\cos \theta )$

The focal chord of a conic perpendicular to axis is 

The locus of a planet orbiting around the sun is: 

The sum of the focal distances of a point on the ellipse $\cfrac { { x }^{ 2 } }{ 4 } +\cfrac { { y }^{ 2 } }{ 9 } =1$ is:

Equation of the ellipse in its standard form is $\displaystyle \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

The focus of extremities of the latus rectum of the family of the ellipse  ${b^2}{x^2} + {a^2}{y^2} = {a^2}{b^2}{\text{ is }}\left( {b \in R} \right)$ 

The equation of the latusrecta of the ellipse $9x^{2}+4^{2}-18x-8y-23=0$ are 

The foci of the ellipse $\dfrac{x^{2}}{16} + \dfrac{y^{2}}{b^{2}} =1$ and the hyperbola $\dfrac{x^{2}}{144} - \dfrac{y^{2}}{81} =\dfrac{1}{25}$ coincide, then the value of $b^{2}$ is: