Circles Test 1...

$$P$$ 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

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 $$(2,3)$$

The equation of the circle passing through $$(3, 6)$$ and whose centre is $$(2, -1)$$ 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 having the lines $$y^{2}+2y+4x-2xy=0$$ as its normals & passing through the point$$(2,1)$$ 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-

If $$2x - 3y = 5$$ and $$3x - 4y = 7$$ are the equation of $$2$$ diameters of a circle whose area is $$88$$ sq. units then the equation of the circle is :

The centres of a set of circles, each of radius $$3$$, lie on the circle $${x}^{2}+{y}^{2}=25$$. The lotus of any point in the set is 

If he equations of two diameters of a circle are $$2x + y = 6$$ and $$3x + 2y = 4$$ and the radius is $$10$$ , find the equation of the circle.