Perfect Square formula - Assignment Example

The Perfect Square formula and its importance in finding the equation of a circle An algebraic equation (quadratic) is solved by completing the square for finding its root(s). The root of a square is always a positive value. By definition, a circle is the set of all points in a plane that lie a given distance from a given point. The given distance is the radius of the circle, and the given point is the center. If we know the center, (h, k) and radius, r of the circle then we can find the circle equation by using the distance formula, as {(x – h)^2 + (y – k)^2}^(1/2) = r.

Squaring both side, we get (x – h)^2 + (y – k)^2 = r^2, which is Center-Radius form of the equation of a circle.Perfect square formula is useful in deciding whether an equation of the form x^2 + y^2 + cx + dy + e = 0, for some real number c, d, and e, can have a graph that is a circle or a point, or is nonexistent. For this, we complete the square to get an equation of the form {(x – h)^2 + (y – k)^2}^(1/2) = m, for some real number m. If the value of m is positive, then the given equation is a circle with radius square root of m.

If the value of m is zero, then the equation represents a single point (h, k). If the value of m is negative, then no points satisfy the equation, and the graph is nonexistent.