Questions: Homework 8 Question 15, 2.4.13 (m, k)=(0,0). Graph the circle. The standard form of the equation of this circle is

Solution Steps

The image presents a geometry problem related to the equation of a circle. The problem states: _Write the standard form of the equation and the general form of the equation of the circle of radius_ $r=10$ _and center_ $(h,k)=(0,0)$. _Graph the circle_.

The standard form of the equation of a circle with radius $r$ and center $(h,k)$ is given by $(x-h)^2+(y-k)^2=r^2$. In this case, $r=10$ and $(h,k)=(0,0)$. Substituting these values into the equation yields $(x-0)^2+(y-0)^2=10^2$, which simplifies to $x^2 + y^2 = 100$.

The general form of the equation of a circle is given by $x^2 + y^2 + Dx + Ey + F = 0$. Since the standard form is $x^2 + y^2 = 100$, we can rewrite this as $x^2 + y^2 - 100 = 0$. This means $D=0$, $E=0$ and $F=-100$.

To graph the circle, we need its center and radius. The center is $(0,0)$, and the radius is $10$. On the Cartesian plane, plot the center at the origin. Then, mark points that are $10$ units away from the center in all directions. These points will lie on the circumference of the circle. Connect these points to form a circle. The graph provided in the image seems to be marked with the correct points, namely $(10,0)$, $(-10,0)$, $(0,10)$, and $(0,-10)$. The grid should depict a circle centered at the origin and with a radius of 10 units.

Final Answer: