# What is the Radius of a Circle whose Equation is x2+y2+8x?6y+21=0?

A circle is a plane figure formed by a set of points at a constant distance from a central point. It has a radius, diameter, chord, tangent, and secant. Learn about the standard and expanded form of circle equations, along with how to calculate the center and radius of a circle.

In this article, we'll solve a question regarding the radius of a circle whose equation is x2+y2+8x?6y+21=0. We'll also look at how the equation can be converted to a quadratic form using the Pythagorean Theorem and an inverse trigonometric function.

The first step in finding the radius of a circle is to shift the origin away from the left side of the equation. This will make the equation more manageable and easier to solve. We'll need to move the origin to a position where the constant term (x2+y2) is completely outside of the variable terms, in this case, (x-3)2/49 + y2/25.

Once the origin is shifted to a position where the constant term is completely outside of the variable terms, we can proceed to reduce the equation to its standard form by performing a perfect square. This will convert the complex number to a simpler form.

The final equation will be x - h - k = r2. To find the radius, we need to divide both sides by 2, so we need to add 4 to each side of the expression. This will give us the value of the radius, which is 5 units.