Conic Sections ...

Two vertices of an equilateral triangle are $$(-1, 0)$$ and $$(1, 0)$$, and its third vertex lies above the $$x$$-axis. The equation of the circumcircle of the triangle is

The length of the latus rectum of the parabola whose focus is $$\left ( 3,3 \right )$$ and directrix is  $$3x-4y-2=0$$ is

The triangle PQR is inscribed in the circle $$\displaystyle x^{2}+y^{2}= 25.$$ If $$Q$$ and $$R$$ have coordinates $$\displaystyle \left ( 3, 4 \right )$$ and $$\displaystyle \left ( -4, 3 \right ),$$ respectively, then $$\displaystyle \angle QPR$$ is equal to

The lines $$\displaystyle 2x - 3y = 5$$ and $$\displaystyle 3x - 4y = 7$$ intersect at the center of the circle whose area is $$154$$ sq. units, then equation of circle is

The equation of circle with origin as a centre and passing through equilateral triangle whose median is of length $$3a$$ is

The equation of a diameter of a circle is $$x+y=1$$ and the greatest distance of any point of the circle from the diameter is $$\dfrac{1}{\sqrt{2}}$$ .Then, a possible  equation of the circle can be

Find the  Lactus Rectum of  $$\displaystyle 9y^{2}-4x^{2}=36$$ 

If the centroid of an equilateral triangle is $$(1, 1)$$ and its one vertex is $$(-1, 2)$$ then the equation of its circumcircle is

The equation $$ \displaystyle 3x^{2}-2xy+y^{2}=0 $$ represents:

The length of the latus rectum of the parabola $$x=ay^2+by+c$$ is