Conic Sections ...

The locus of a point which moves such that the sum of the squares of its distances from three vertices of a triangle ABC is constant is a circle
whose centre is at the

The lines 2x-3y $$=5$$ and 3x-4y $$=7$$ diameters of a circle having area as $$154$$ units. Then the equation of the circle is:

lf the line $$3{x}-2{y}+6=0$$ meets $${x}$$-axis, $$y$$-axis respectively at $${A}$$ and $${B}$$, then the equation of the circle with radius $${A}{B}$$ and Centre at $${A}$$ is

lf the lines $$2x+3y+1=0$$ and $$3x-y-4=0$$ lie along diameters of a circle of circumference $$ 10\pi$$, then the equation of the circle is:

lf the lines $$2x-3y=5$$ and $$3x-4y=7$$ are two diameters of a circle of radius $$7$$ then the equation of the circle is

The equation of the image of the circle $$x^{2}+y^{2}-6x-4y+12=0$$ by the line mirror $$x+y-1=0$$ is

The area of a circle centered at $$(1,2)$$ and passing through $$(4,6)$$ is

A line is at a constant distance $$c$$ from the origin and meets the coordinates axes in $$A$$ and $$B$$. The locus of the centre of the circle passing through $$O, A, B$$ is

The equation of the circle passing through the point $$(-1,2)$$ and having two diameters along the pair of lines $$\mathrm{x}^{2}-\mathrm{y}^{2}-4\mathrm{x}+2\mathrm{y}+3=0$$ is

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