The identification of circles is about discerning a spherical geometric figure in which all points are equally distant from a central point. It's important to be aware of certain features such as the center, the radius (which is the measurement from the center to the periphery of the circle), and the diameter (which is twice the radius and spans across the circle through its center).
| Topic | Problem | Solution |
|---|---|---|
| None | $x^{2}+y^{2}-8 x+16 y-1=0$ is the equation of a c… | The given equation is \(x^{2}+y^{2}-8 x+16 y-1=0\). |
| None | Find the center and the radius of the circle. The… | The given equation is already in the standard form of a circle equation, which is \(x^{2}+y^{2}=r^{… |
| None | A circle has the equation $(x-4)^{2}+(y+7)^{2}=10… | The equation of a circle is given by \((x-h)^2 + (y-k)^2 = r^2\) where \((h, k)\) is the center of … |
| None | $x^{2}+y^{2}-10 x-2 x+17=0$ | Rewrite the equation as \(x^2 - 12x + y^2 - 10y + 17 = 0\) |
| None | Find the center and radius of the circle represen… | \( (x-h)^{2} + (y-k)^{2} = r^{2} \) |