Complete the Square and Graph the Circle x^2 + y^2 - 2x - 6y - 26 = 0 MyMathlab

TL;DR

Simplify given equation, complete the square, find center & radius, graph circle.

Transcript

in this video we have to write the equation of the circle in standard form the equation given is x squared plus y squared minus 2x minus 6y minus 26 equals 0 so the first thing you have to do in these problems is you want to group together all of the X's and group together all of the Y's so we write it again as x squared minus 2x and grouping toget... Read More

Key Insights

• 🍉 Group X's and Y's, add constant term, complete the square for circle equations.
• 🤘 Center is identified by switching signs, radius is square root of constant term.
• 📈 Graphing the circle visually represents the equation and its properties.

Questions & Answers

Q: How do you simplify the given circle equation into standard form?

To simplify, group X's and Y's, add a constant term, complete the square by halving and squaring coefficients, then identify the center and radius of the circle.

Q: What is the significance of completing the square in finding the equation of a circle?

Completing the square helps in converting the given equation to standard form, making it easier to identify the center and radius of the circle accurately.

Q: How do you find the center and radius of a circle from the standard form equation?

The center is given by switching the signs of the completed square terms, and the radius is the square root of the constant term after completing the square.

Q: Why is graphing the circle important after finding the equation?

Graphing the circle visually represents the equation, allowing for better understanding of its properties such as center, radius, and overall shape.

Summary & Key Takeaways

• Identify X's and Y's, group them, add a constant term.

• Complete the square by halving and squaring coefficients.

• Determine center (1,3), radius (6), and graph the circle.