Find the equation of the tangent to the circle x2 + y2 = 16 drawn from the point (1, 4).
Given circle is
x2 + y2 = 16 …(i)
Any tangent of (i) in terms of slope is
Which passes through (1, 4)
From (ii), equation of tangent drawn from (1, 4) are
Find the equation of the circle passing through the points of intersection of the circles x2 + y2 – 2x – 4y – 4 = 0 and x2 + y2 – 10x – 12y – 40 = 0.
Find the equation of circle through points of intersection of circle x2 + y2– 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x + 2y = 0.
Find the angle between the circles. S = x2 + y2 – 4x + 6y + 11 = 0 and
Find the equation of the system of circles coaxial with the circles.
x2 + y2 + 4x + 2y + 1 = 0, x2 + y2 – 2x + 6y – 6 = 0
Also find the equation of that particular circle whose centre lies on radical axis.
Find the locus of pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.
Find the circle whose diameter is the common chord of the circles
x2 + y2 + 2x + 3y + 1 = 0 and x2 + y2 + 4x + 3y + 2 = 0
S ≡ x2 + y2 + 2x + 3y + 1 = 0 S’ ≡ x2 + y2 + 4x + 3y + 2 = 0
Find the equation of circle which cuts the circle x2 + y2 + 5x + 7y + 4 = 0 orthogonally, has its centre on the line x = 2, and passes through the point (4, –1).
Find the point of intersection of the line 2x + 3y = 18 and the circle x2 +y2 = 25.
Find the equation of the normal to the circle x2 + y2 – 5x + 2y – 48 = 0 at point (5, 6).
Find the equation of the image of the circle x2 + y2 + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0.