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.
Equation of chord of contact AB is
hx + ky = a2 …(1)
for equation of pair of tangent of OA and OB, make homogeneous x2 +y2 = a2 with the help of hx + ky = a2 or
The line (x – 2) cos θ + (y – 2) sin θ = 1 touches a circle for all values of θ. Find the circle.
Find the equation of the normal to the circle
x2 + y2 – 5x + 2y – 48 = 0 at the point (5, 6).
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.
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.