Circles Questions (554)

The equation of the circle having centre (1, -2) and passing through the point of intersection of lines 3x + y = 14, 2x + 5y = 18 is

The equation of the circle passing through (1, 2) and the points of intersection of the circles x2 + y2 - 8x - 6y + 21 = 0 and x2 + y2 - 2x - 15 = 0 is

AP and BQ are fixed parallel tangents to a circle, and a tangent at any point C cuts them at P and Q respectively. Show that CP · CQ is independent of the position of C on the circle and ∠POQ is a right angle. Let the parallel tangents touch the circle at M and N respectively. Then MN is a diameter through the centre O. Prove that CP · CQ = a² = constant.

Find the slope(s) of the tangent(s) drawn from the origin to the circle \((x-3)^2 + (y-3)^2 = 6\).