Is the equation $\frac{{(x + 3)}^{2}}{4} + \frac{{(y - 2)}^{2}}{4} = 1$ $(x+3)^2 /4 + (y -2)^2 / 4 =1$ a line, parabola, ellipse, hyperbola, or circle?

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Answer 1 · 2015-11-24T23:56:29

A circle.

Multiply everything by $4$ $4$ to see that:

${(x + 3)}^{2} + {(y - 2)}^{2} = 4$ $(x+3)^2+(y-2)^2=4$

This is in the form of a circle ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ $(x-h)^2+(y-k)^2=r^2$ .

The circle has a center at $(- 3, 2)$ $(-3,2)$ and a radius of $2$ $2$ .

Is the equation (x+3)24+(y−2)24=1(x+3)^2 /4 + (y -2)^2 / 4 =1 a line, parabola, ellipse, hyperbola, or circle?