Question

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

Solution

Correct option is

None of these

 

Given circle  

                   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

                  + 2y = λ 

Since normal passes through the centre of the circle i.e. (1, 0) 

Then             1 + 0 = λ  

∴                          λ = 1

The equation of normal is

                     x + 2y = 1

or                 x + 2y – 1 = 0  

SIMILAR QUESTIONS

Q1

Find the equation of the circle which passes through the origin and makes intercepts of length a and b on axis of x and y respectively.

Q2

A circle of radius 2 lies in the first quadrant and touches both the axes of coordinate. Find the equation of circle with centre at (6, 5) and touching the above circle externally.

Q3

A circle of radius 5 units touches the coordinates axes in 1st quadrant. If the circle makes one complete roll on x axis along positive direction of xaxis. Find the equation in new position. 

Q4

 

Discus the position of the points (1, 2) and (6, 0) with respect to the circle.

                 x2 + y2 – 4x + 2y – 11 = 0   

Q5

 

Find the shortest and largest distance from the point (2, –7) to the circle 

                 x2 + y2 – 14x – 10y – 151 = 0   

Q6

Find the length of intercept on the S.L. 4x – 3y – 10 = 0 by the circle x2y2 – 2x + 4y – 20 = 0.

Q7

Find the coordinates of the middle point of the chord which the circle x2y2 + 4x – 2y – 3 = 0 cut off the line x – y + 2 = 0.   

Q8

For what values of λ will the line y = 2x + λ be a tangent to the circle x2y2 = 5.

Q9

Find the equation of tangent to the circle x2 + y2 – 2ax = 0 at the point  

Q10

 

Find the equation of normal at the point (5, 6) to the circle;

x2 + y2 – 5x + 2y – 48 = 0