Question

Find the equation of the normal to the circle x2 + y2 = 2x, which is parallel to the line x + 2y = 3.

Solution

Correct option is

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

SIMILAR QUESTIONS

Q1

Find the angle between the circles. S = x2 + y2 – 4x + 6y + 11 = 0 and 

Q2

 

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.

Q3

Find the locus of pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.

Q4

 

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

Q5

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).

Q6

Find the point of intersection of the line 2x + 3y = 18 and the circle x2 +y2 = 25.

Q7

Find the equation of the normal to the circle x2 + y2 – 5x + 2y – 48 = 0 at point (5, 6).

Q8

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

Q9

Find the equation of the image of the circle x2 + y2 + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0.

Q10

 

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.