Find The Equation Of The Chord x2 + y2 – 6x + 10y – 9 = 0 Which Is Bisected At (–2, 4).

Find the equation of the tangents to the circle x² + y² = 16 drawn from the point (1, 4).

The angle between a pair of tangents from a point P to the circle x² + y²+ 4x – 6y + 9 sin²α + 13 cos²α = 0 is 2α. Find the equation of the locus of the point P.

Find the length of the tangents drawn from the point (3, – 4) to the circle 2x² + 2y² – 7x – 9y – 13 = 0.

Find the area of the triangle formed by tangents from the point (4, 3) to the circle x² + y² = 9 and the line segment joining their points of contact is 

Find the length of the tangent from any point on the circle x² + y² + 2gx+ 2fy + c = 0 to the circle x² + y² + 2gx + 2fy + c₁ = 0 is

Find the power of point (2, 4) with respect to the circle 

                x² + y² – 6x + 4y – 8 = 0

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