If a circle passes through points $$(4,0)$$ and $$(0,2)$$ and its centre lies on $$\mathrm{Y}$$-axis. If the radius of the circle is $$r$$, then the v...

Number of common tangents to the circles $$x^2+y^2-6 x-14 y+48=0$$ and $$x^2+y^2-6 x=0$$ are

The parametric equations of the circle $$x^2+y^2+2 x-4 y-4=0$$ are

If the circles $$x^2+y^2=9$$ and $$x^2+y^2+2 \alpha x+2 y+1=0$$ touch each other internally, then the value of $$\alpha^3$$ is

The sides of a rectangle are given by the equations $$x=-2, x=4, y=-2$$ and $$y=5$$ Then the equation of the circle, whose centre is the point of inte...

Two tangents to the circle $$x^2+y^2=4$$ at the points $$\mathrm{A}$$ and $$\mathrm{B}$$ meet at the point $$\mathrm{P}(-4,0)$$. Then the area of the ...

The equation of circle with centre at $$(2,-3)$$ and the circumference $$10 \pi$$ units is

The equation of the circle whose centre lies on the line $$x-4 y=1$$ and which passes through the points $$(3,7)$$ and $$(5,5)$$ is

If the lines $$3x - 4y + 4 = 0$$ and $$6x - 8y - 7 = 0$$ are tangents to a circle, then the radius of the circle is