Find the locus of pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.
y(lx – h) = mx2
Let the centre be (h, 0)
Equation S ≡ (x – h)2 + (y)2 = h2
or x2 + y2 – 2xh = 0
Let the pole be (x1, y1) then polar with respect to circle
Identical with lx + my + n = 0
So locus of pole (x1, y1)
If y(lx – h) = mx2.
If two tangents are drawn from a point on the circle x2 + y2 = 25 to the circle x2 + y2 = 25. Then find the angle between the tangents.
Find the equation of diameter of the circle x2 + y2 + 2gx + 2fy + c = 0 which corresponds o the chord ax + by + λ = 0.
Examine if the two circle x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 touch each other externally or internally. Also the pointed contact.
Find the equation of the circle passing through (1, 1) and the point of intersection of circles.
x2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0
Find the equation of circle passing through the point of intersection of the circle x2 + y2 – 6x + 2y + 4 = 0 and x2 + y2 + 2x – 4y – 6 = 0 and whose centre lies on the line y = x.
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 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