Write the equation of a circle given the center and tangent to origin

The video tutorial explains the equation of a circle, focusing on its center and radius. It discusses how to graph a circle and the concept of tangency, where a circle touches the origin at a single point. The tutorial further explores the concept of radius, emphasizing its uniformity around the circle. It concludes with a calculation of the radius using the Pythagorean theorem, demonstrating how to find the radius when given specific coordinates.

What is the general form of a circle's equation?

• (x + h)^2 + (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• x^2 - y^2 = r^2

• x^2 + y^2 = r^2

What does it mean for a circle to be tangent to a point?

• It passes through the point at two places.

• It touches the point at exactly one place.

• It intersects the point at multiple places.

• It does not touch the point at all.

If a circle is tangent to the origin, what can be said about its radius?

• The radius is zero.

• The radius is equal to the distance from the center to the origin.

• The radius is half the distance from the center to the origin.

• The radius is infinite.

How can the radius of a circle be calculated if the center is at (-4, 3) and it is tangent to the origin?

• By measuring directly on a graph

• Using the formula r = √(x^2 + y^2)

• By guessing based on the circle's size

• Using the Pythagorean theorem

What is the radius of a circle with a center at (-4, 3) that is tangent to the origin?

• 3

• 4

• 5

• 6