Find the lengths of common tangents of the circles x2 + y2 = 6x and x2 +y2 + 2x = 0.
Equation of given circles are x2 + y2 = 6x and x2 + y2 + 2x = 0. The given equations of circles can be re-written as
(x – 3)2 + y2 = 9 and (x + 1)2 + y2 = 1
Centres and radii of the given circles are C1(3, 0), r1 = 3 and
C2(–1, 0), r2 = 1 respectively.
Circles touch to each other
Here internal tangent is impossible, only external tangent is possible.
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 external and internal common tangents to two circlesx2 + y2 + 14x – 4y + 28 = 0 and x2 + y2 – 14x + 4y – 28 = 0.
Find the equation of the circle circumscribing the triangle formed by the lines:
x + y = 6, 2x + y = 4 and x + 2y = 5,
Without finding the vertices of the triangle.