The equations of two diameters of a circle are x + y = 6 and x + 2y = 4. If its radius be 10 units, find the equation of the circle.

The centre of a circle is the point (3, 2) and it makes an intercept of length 5 units on the X-axis. Find the equation of the circle.

Find the equation of the diameter of the circle x ^2 + y ^2 - 14x + 6y + 9 = 0 which passes through the point (2, 1).

Find the equations of two tagents to the circle x ^2 + y ^2 = 34 which are parallel to the straight line 5y - 3x + 7 = 0.

Two extremities of a diameter of a circle are (-4, 3), (12, -1). Find the length of the chord made by the circle on the Y -axis.

Find the equation of two lines parallel to 5x -12y + 26 = 0 at a distance of 4 units from it.

Show that x + y = 1 is the equation of the line of a diameter of the circle x ^2 + y ^2 - 4x + 2y + 1 = 0

Find the equation of the tangents to the circle x ^2 + y ^2 - 2x - 4y - 4 = 0 which are perpendicular to the line 3x - 4y - 1 = 0

The radius of two circles are in the ratio 3 : 4 and sum of their areas is equal to the area of a circle whose radius is 35 cm. Find the radius of these two circles.

The area of the region between two concetric circles is 770cm^2 If the radius of the greater circle is 21 cm.Find the radius of the smaller circle.

Find the equation of the circle concentric with the circle x ^2 + y ^2 - 8x + 12y + 15 = 0 and passing through the point (5, 4).