Conic Sections ...

Vertex of the parabola $$9x^2 - 6x + 36y + 9 = 0$$ is

If two vertices of an equilateral triangle are $$A (-a, 0)$$ and $$B(a, 0), a > 0$$ and the third vertex C lies above x-axis then the equation of the circumcircle of $$\Delta ABC$$ is

The equation(s) of the circle(s) which pass through the ends of the common chords of two circles $$2x^{2}+2y^{2}+8x+4y-7=0$$ and $$x^{2}+y^{2}-8x-4y-5=0$$ and touch the line $$x=7$$ is (are) :

The equation of the circle which touches the axes of $$y$$ at the origin and passing through $$(3,4)$$ is

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 value of k, such that the equation 
$$2x^{2}+2y^{2}-6x+8y+k=0$$ represent a point circle , is 

If the radius of the circle $$x^{2}+y^{2}-18x-12y+k=0$$ be $$11$$ then k=

The equation of a circle which is passing through the vertices of an equilateral triangle whose median is of length 3 a is

Equation $$\sqrt{(x-2)^2 + y^2} + \sqrt{(x+2)^2 + y^2}$$ = 4 represents _____________.

If $$\left| z-{ z }_{ 0 } \right| =\dfrac { \left| a\overline { z } +a\overline { z } +b \right|  }{ 2\left| a \right|  } $$ represent a parabola, Then the  length of latus  rectum of parabola