If the lines $3 x-4 y+4=0$ and $6 x-8 y-7=0$ are the tangents to the same circle, then the area of that circle (in sq. units) is

Circles are drawn through the point $(2,0)$ to cut intercepts of length 5 units on the $X$-axis. If their centre lie in the first quadrant, then their equation is

If $A(\cos \alpha, \sin \alpha), B(\sin \alpha,-\cos \alpha), C(1,2)$ are the vertices of a $\triangle A B C$, then the locus of its centroid is

A circle passing through origin cuts the coordinate axes is $A$ and $B$. If the straight line $A B$ passes through a fixed point $\left(x_1, y_1\right)$, then the locus of the centre of the circle is