(x+1)^2+(y-3)^2=49

3 min read Jun 16, 2024
(x+1)^2+(y-3)^2=49

Unveiling the Secrets of (x+1)^2 + (y-3)^2 = 49

The equation (x+1)^2 + (y-3)^2 = 49 represents a circle in the Cartesian coordinate system. Let's dive into its properties and understand how to interpret this equation.

The Standard Equation of a Circle

The general standard form for the equation of a circle is:

(x - h)^2 + (y - k)^2 = r^2

Where:

  • (h, k) represents the center of the circle.
  • r represents the radius of the circle.

Analyzing our Equation

Comparing our equation (x+1)^2 + (y-3)^2 = 49 to the standard form, we can identify the following:

  • Center: (h, k) = (-1, 3)
  • Radius: r^2 = 49 => r = 7

Visualizing the Circle

With the center and radius in hand, we can easily visualize the circle on a graph:

  1. Plot the center: Locate the point (-1, 3) on the coordinate plane.
  2. Draw the circle: Starting from the center, draw a circle with a radius of 7 units.

Key Points to Remember

  • The equation (x+1)^2 + (y-3)^2 = 49 describes a circle with its center at (-1, 3) and radius of 7 units.
  • The standard form of the circle equation is a powerful tool for understanding and graphing circles.
  • Understanding the relationship between the equation and its corresponding geometric shape allows for deeper insights into mathematical concepts.

By analyzing the equation (x+1)^2 + (y-3)^2 = 49, we have unveiled the hidden properties of this circle. This journey helps us appreciate the connection between algebraic equations and geometric figures.

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