Find the lengths of external and internal common tangents to two circlesx2 + y2 + 14x – 4y + 28 = 0 and x2 + y2 – 14x + 4y – 28 = 0.
External = 14 & Internal = 4
The given circles
Centres and radii of circles S1 and S2 are C1(–7, 2),
Hence circles don’t touch or cut.
∴ Length of external common tangent
and length of internal common tangent
Find the equations of the two circles which intersect the circles
x2 + y2 – 6y + 1 = 0 and x2 + y2 – 4y + 1 = 0
Orthogonally and touch the line 3x + 4y + 5 = 0.
Find the radical centre of circles x2 + y2 + 3x + 2y + 1 = 0,
x2 + y2 – x + 6y + 5 = 0 and x2 + y2 + 5x – 8y + 15 = 0. Also find the equation of the circle cutting them orthogonally.
Find the radical centre of three circles described on the three sides 4x – 7y + 10 = 0, x + y – 5 = 0 and 7x + 4y – 15 = 0 of a triangle as diameters.
Find the co-ordinates of the limiting points of the system of circles determined by the two circles
x2 + y2 + 5x + y + 4 = 0 and x2 + y2 + 10x – 4y – 1 = 0
If the origin be one limiting point of a system of co-axial circles of whichx2 + y2 + 3x + 4y + 25 = 0 is a member, find the other limiting point.
Find the radical axis of co-axial system of circles whose limiting points are (–1, 2) and (2, 3).
Find the equation of the circle which passes through the origin and belongs to the co-axial of circles whose limiting points are (1, 2) and (4, 3).
Find the equation of the image of the circle x2 + y2 + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0.
Find the area of the triangle formed by the tangents drawn from the point (4, 6) to the circle x2 + y2 = 25 and their chord of contact. Also find the length of chord of contact.
Find the lengths of common tangents of the circles x2 + y2 = 6x and x2 +y2 + 2x = 0.