The circle x^2 + y^2 - 8x + 4y + 4 = 0 touches - Vidyadip

MCQ

The circle ${x^2} + {y^2} - 8x + 4y + 4 = 0$ touches

A
$x$-axis only
✓
$y$- axis only
C
Both $x$ and $y$- axis
D
Does not touch any axis

✓

Answer

Correct option: B.

$y$- axis only

b
(b) The given equation can be written as ${(x - 4)^2} + {(y + 2)^2} = {4^2}$.

We know that the standard equation of the circle with centre $(h, k)$ is ${(x - h)^2} + {(y - k)^2} = {r^2}.$

Comparing the given equation with the standard equation, we get centre $\equiv $ $(4,\, - 2)$ and radius = $4$.

Since co-ordinates of the centre of the circle are $(4,\, - 2)$, therefore the given circle touches $y$-axis only.

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