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Question

The circle passing through (1,-2) and touching the X-axis at(3,0), also passes through the point


A

(-5,2)

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B

(2,-5)

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C

(5,-2)

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D

-2,5

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Solution

The correct option is C

(5,-2)


Explanation for the correct answer:

Finding the equation of the circle:

Given points: (1,-2) and touching the x-axis at(3,0).

The equation of the required circle is x-32+y2+λy=0

As the point, (1,-2) satisfies the equation, we have

4+4=2λ λ=4

Therefore the equation of the circle is

x-32+y2+4y=0x2-6x+9+y2+4y=0x2+y2-6x+4y+9=0

On trial and error basis, we get (5,-2) satisfies the obtained equation and satisfy the conditions.

Therefore, the correct answer is option (C).


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