The area of the curve $x^2 + y^2 = 2ax$ is

If the angle between the circles $x^2+y^2-12x-6y+41=0$ and $x^2+y^2+kx+6y-59=0$ is $45^{\circ}$,then a value of $k$ is

The intercept on the line $y = x$ by the circle $x^2 + y^2 - 2x = 0$ is $AB$. The equation of the circle with $AB$ as a diameter is . . . . . .

In an acute-angled $\triangle ABC$,the altitudes from $A, B, C$ when extended intersect the circumcircle again at points $A_1, B_1, C_1$ respectively. If $\angle ABC = 45^{\circ}$,then $\angle A_1 B_1 C_1$ equals (in $^{\circ}$)

Find the maximum distance of the point $K(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$.

For how many values of $p$ does the circle $x^2+y^2+2x+4y-p=0$ and the coordinate axes have exactly three common points?