The circle passing through (1, -2) and touching the axis of x at (3, 0) also passes through the point (1) (2, -5) (2) (5, -2) (3) (-2, 5) (4) (-5, 2)

Options

A. (-5, 2)
B. (2, -5)
C. (5, -2)
D. (-2, 5)

Answer

A

Explanation

The equation of the circle touching x-axis i.e. y=0 at (3, 0) is
`(x-3)^(2)+(y-0)^(2) + lambda y = 0 ` ...(i)
It passes through (1, -2).
`:. (1-3)^(2) + (2-0)^(2)-2 lambda = 0 lambda = 4`
Putting `lambda = 4 ` in (i), we obtain
`(x-3)^(2)+y^(2)+4y=0 or, x^(2)+y^(2)-6x+4y+9=0`
Clearly, it passes through (5, -2).