Conic Sections ...

A circle is concentric with circle $$x^{2}+ y^{2}-2x+4y-20=0$$. If perimeter of the semicircle is $$36$$ then the equation of the circle is :

The axes are translated so that the new equation of the circle $$x^{2}+y^{2}-5x+2y-5=0$$ has no first degree terms. Then the new equation is

vertices of an ellipse are $$(0,\pm 10)$$ and its eccentricity $$e=4/5$$ then its equation is 

The name of the conic represent by the equation $$x^2+y^2-2y+20x+10=0$$ is

The equation of the circle passing through the foci of the ellipes  $${\frac{x}{{16}}^2} + {\frac{y}{{{9^{}}}}^2} = 1$$ and having centre at $$\left( {0,3} \right)$$ is 

The equation of ellipse whose major axis is along the direction of x-axis, eccentricity is $$e=2/3$$

The equation $$\dfrac { x ^ { 2 } } { 10 - a } + \dfrac { y ^ { 2 } } { 4 - a } = 1$$ represents an ellipse if

Consider the set of hydperbola $$xy=k,k\ \in\ R$$. Let $$e_{1}$$ be the eccentricity when $$k=4$$ and $$e_{2}$$ be the eccentricity when $$k=9$$ . Then $$e^{2}_{1}+e^{2}_{2}=$$

If a circle with centre $$(0,0)$$ touches the line $$5x+12y=1$$ then it equation will be

If there is exactly one tangent at a distance of $$4$$ units from one of the locus of $$\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{a^{2}-16}=1, a>4$$, then length of latus rectum is :-