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The circle $x 2 + y 2 + 2 x − 4 y + 1 = 0$ touches

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X-axis

Y-axis

Both axes

None of these

answer is A.

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Detailed Solution

It’s given that the equation of the circle is

x 2 + y 2 + 2 x − 4 y + 1 = 0

. We transform it in its general form of

(x − α) 2 + (y − β) 2 = r 2

and get

(x − 1) 2 + (y − 2) 2 = 22

. O is the centre.
Equating with the general equation of circle

(x − α) 2 + (y − β) 2 = r 2

, we get the centre as O = (−1, 2) and the radius as 2 units.
seo

We get that if it touches any axes then we can put the x and y coordinates as 0 and get only 1 value for the other coordinate. If we get no solutions or two solutions, then we can say it doesn’t touch the axes.
We put x = 0 and get

(y − 2) 2 = 3

which gives

y = 2 ± 3

. The circle doesn’t touch the Y-axis. It intersects at two points.
Now if we put y = 0 and get

(x + 1) 2 = 0

which gives x = −1. The circle touches the X-axis at point A = (−1, 0).

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