Find the equation of the normal to the circle x2 + y2 = 2x, which is parallel to the line x + 2y = 3.
x + 2y – 1 = 0
Given circle is x2 + y2 – 2x = 0
Centre of given circle is (1, 0)
Since normal is parallel to x + 2y = 3
Let the equation of normal is x + 2y = λ
Since normal passes through the centre of the circle i.e., (1, 0)
Then 1 + 0 = λ
∴ λ = 1
Then equation of normal is x + 2y = 1
or x + 2y – 1 = 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 tangent to the circle x2 + y2 = 16 drawn from the point (1, 4).
Find the equation of the image of the circle x2 + y2 + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0.
Find the equation of the circle which cuts orthogonally each of the three circles given below:
x2 + y2 – 2x + 3y – 7 = 0, x2 + y2 + 5x – 5y + 9 = 0 and x2 + y2 + 7x – 9x + 29 = 0.