Writing standard equation of a circle | Mathematics II | High School Math | Khan Academy

TL;DR

Find the equation of a circle with a given center and a point on the circle.

Transcript

• [Voiceover] So we have a circle here and they specified some points for us. This little orangeish, or, I guess, maroonish-red point right over here is the center of the circle, and then this blue point is a point that happens to sit on the circle. And so with that information, I want you to pause the video and see if you can figure out the equati... Read More

Key Insights

• ⭕ The equation of a circle can be found given its center and a point on the circle.
• 😥 The center of the circle is determined by the coordinates of a given point.
• ⭕ The radius of the circle can be calculated by finding the distance between the center and any point on the circle.
• ❓ The distance formula, derived from the Pythagorean Theorem, can be used to calculate the radius.
• 📤 The equation of a circle is in the form (x + a)^2 + (y + b)^2 = r^2, with (a, b) representing the coordinates of the center and r being the radius.
• 💱 The absolute value of the change in x and y can be used in the distance formula, as squaring them eliminates the negative sign.
• ⭕ Simplifying the equation of the circle involves subtracting a negative, which becomes a positive.

Questions & Answers

Q: How do you find the center of a circle?

The center of a circle is determined by the coordinates of a given point. For example, if the point is (-1, 1), then the center of the circle is (-1, 1).

Q: How can the radius of the circle be calculated?

The radius of the circle can be calculated by finding the distance between the center and any point on the circle. This can be done using the distance formula, which is derived from the Pythagorean Theorem.

Q: What is the formula for the equation of a circle?

The formula for the equation of a circle is (x + a)^2 + (y + b)^2 = r^2, where (a, b) represents the coordinates of the center and r is the radius of the circle.

Q: How can the radius be determined using the Pythagorean Theorem?

By setting up a right triangle with the center, any point on the circle, and a line connecting them, the distance formula (derived from the Pythagorean Theorem) can be used to find the length of the line, which represents the radius of the circle.

Summary & Key Takeaways

• The video discusses how to find the equation of a circle given its center and a point on the circle.

• The center of the circle is determined by the coordinates of a given point.

• The radius of the circle can be found by calculating the distance between the center and any point on the circle.