Find The Locus Of The Pole Of The Line lx + my + n = 0 With Respect To The Circle Which Touches y-axis At The Origin.

Show that the locus of the point, the powers of which with respect to two given circles are equal, is a straight line.

Find the condition that chord of contact of any external point

(h, k) to the circle x² + y² = a² should subtend right angle at the centre of the circle.

The chord of contact of tangents drawn from a point on the circle x² +y² = a² to the circle x² + y² = b² touches the circle x² = y² = c². Show that a, b, c are in GP.

Find the equation of the chord x² + y² – 6x + 10y – 9 = 0 which is bisected at (–2, 4).

Find the middle point of the chord intercepted on line lx + my + n = 0 by the circle x² + y² = a².

Find the locus of middle points of chords of the circle x² + y² = a², which subtend right angle at the point (c, 0).

Find the equations of the tangents from the point A(3, 2) to the circle x²+ y² + 4x + 6y + 8 = 0 .

If two tangents are drawn from a point on the circle x² + y² = 50 to the circle x² + y² = 25 then find the angle between the tangents.

Find the equation of the diameter of the circle

x² + y² + 2gx + 2fy + c = 0 which corresponds to the chord ax = by + d= 0.

Examine if the two circles x² + y² – 2x – 4y = 0 and x² + y² – 8y – 4 = 0 touch each other externally or internally.