If you're looking to determine a circle by using a central point and another point, two crucial pieces of information are required: the center coordinates, denoted as (h,k), and the coordinates of the point that resides on the circle, represented as (x,y). The radius of the circle is essentially the distance between these two points. To solve this, apply the equation for a circle, which is (x-h)²+(y-k)²=r².
| Topic | Problem | Solution |
|---|---|---|
| None | Write the equation of the circle in the form $(x-… | The general form of the equation of a circle is \(x^{2}+y^{2}+2gx+2fy+c=0\). Comparing this with th… |
| None | $x^{2}+y^{2}-8 x+16 y-1=0$ is the equation of a c… | The general equation of a circle is given by \((x-h)^2 + (y-k)^2 = r^2\). Comparing this with the g… |
| None | Write the standard form of the equation of the ci… | The standard form of the equation of a circle is given by \((x-h)^2 + (y-k)^2 = r^2\), where \((h, … |
| None | Write the standard form of the equation of the ci… | The standard form of the equation of a circle is given by \((x-a)^2 + (y-b)^2 = r^2\), where \((a, … |
| None | Find the center and radius of the circle represen… | Complete the square for both x and y terms: \((x^2 - 18x) + (y^2 + 10y) = -25\) |