The area of the circle centered at $(1, 2)$ and passing through $(4, 6)$ is

The length of the chord intercepted by the circle $x^2 + y^2 = 1$ on the line $x + y = 1$ is:

If the ratio of the lengths of the tangents drawn from the point $(1, 2)$ to the circles $x^2 + y^2 + x + y - 4 = 0$ and $3x^2 + 3y^2 - x - y + k = 0$ is $4 : 3$,then $k = \dots$

Among all the parallelograms whose diagonals are $10$ and $4$,the one having maximum area has its perimeter lying in the interval

The number of circles that touch all the straight lines $x+y=4$,$x-y=-2$,and $y=2$ is

Find the equation of a circle that touches the $Y$-axis at a distance of $4$ units from the origin and cuts an intercept of $6$ units on the $X$-axis.