MarkFL said:The equation of a circle centered ar $(h,k)$ is given by:
\(\displaystyle (x-h)^2+(y-k)^2=r^2\)
If the circle is tangent to the $x$-axis, then its radius must be $r=|k|\implies r^2=k^2$, thus we have:
\(\displaystyle (x-h)^2+(y-k)^2=k^2\)
We are given $(h,k)=(3,5)$, so plug in those numbers. :D
The equation of a circle is a mathematical representation that describes all the points on a circle's circumference. It is written in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.
To find the center and radius of a circle from its equation, you can compare it to the standard form (x - h)^2 + (y - k)^2 = r^2. The values of h and k will give you the coordinates of the center, and the value of r will give you the radius.
The equation of a circle and its graph are closely related. The equation can be used to plot points on the circle's circumference and to determine its center and radius. The graph, in turn, helps visualize the circle and its properties.
A general equation of a circle is written in the form (x - a)^2 + (y - b)^2 = r^2, where (a, b) represents the center and r represents the radius. A standard equation of a circle is written in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center and r represents the radius. The only difference is the use of different variables for the center of the circle.
The equation of a circle has many real-world applications, such as in engineering, architecture, and physics. It can be used to design circular structures, calculate the orbit of planets and satellites, and analyze the shape and size of circular objects. It is also used in GPS systems and other navigation technologies to determine the distance and location of objects.