Conic Sections ...

Two rods of lengths 'a' and 'b' slide along coordinate aces such that their ends are concyclic. Locus of the centre of the circle is?

The length of the diameter of the circle which touches the $$x-$$axis at the point $$(1,0)$$ and passes through the point $$(2,3)$$

$$P$$ and $$Q$$ are any two points on the circle $$x^2 + y^2 = 4$$ such that $$PQ$$ is a diameter. If $$\alpha$$ and $$\beta$$ are the lengths of perpendicular from $$P$$ and $$Q$$ on $$x + y = 1$$ then the maximum value of $$\alpha \beta$$ is

The circle passing through the points $$(-1,0)$$ and touching the y-axis at $$(0,2)$$ also passes through the point:

The equation of the circle passing through $$(3, 6)$$ and whose centre is $$(2, -1)$$ is

If $$(6, -3)$$ is the one extremity of diameter to the circle $$x^{2}+y^{2}-3x+8y-4=0$$ then its other extremity is-

The equation of circle with centre $$(1,2)$$ and tangent $$x+y-5=0$$ is

Eccentricity of an ellipse is $$\sqrt {\cfrac{2}{5}} $$ and it passes through the point $$(-3,1)$$ then its equation is 

The equation of the circle having the lines $$y^{2}+2y+4x-2xy=0$$ as its normals & passing through the point$$(2,1)$$ is

The circle $${x^2} + {y^2} - 3x - 4y + 2 = 0$$ cuts $$x$$-axis