Find The Equation Of The Normal To The Circle x2 + y2 = 2x, Which Is Parallel To The Line x + 2y = 3.

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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

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