Finding Equations of Tangents to a Circle

This video tutorial explains how to find the equation of a tangent to a circle. It begins with an introduction to tangents and the setup of an example problem. The video then covers the circle equation and how to calculate the radius. A three-step process is detailed for finding the tangent equation, including calculating the gradient of the radius and tangent. The tutorial concludes with solving the tangent equation and encouraging practice.

What is a tangent to a circle?

• A line that intersects the circle at two points

• A line that passes through the center of the circle

• A line that touches the circle at exactly one point

• A line that is parallel to the circle

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

• x^2 + y^2 = r^2

• x^2 - y^2 = r^2

• x^2 + y^2 = r

• x + y = r^2

How do you find the radius from the equation x^2 + y^2 = 25?

• Divide 25 by 2

• Multiply 25 by 2

• Subtract 5 from 25

• Take the square root of 25

What is the first step in finding the equation of a tangent?

• Find the y-intercept of the tangent

• Calculate the gradient of the radius

• Identify the center of the circle

• Determine the length of the radius

How do you find the gradient of the tangent if you know the gradient of the radius?

• Add 1 to the gradient of the radius

• Multiply the gradient of the radius by 2

• Take the negative reciprocal of the gradient of the radius

• Square the gradient of the radius

What is the final step in determining the equation of the tangent?

• Determine the circumference of the circle

• Calculate the area of the circle

• Substitute the known point into the line equation

• Find the midpoint of the radius

What is the y-intercept of the tangent line in the example provided?

• 4

• 25/4

• 5

• 25