Tangent Lines and Gradients

This video tutorial explains how to find the equation of a tangent to a circle. It covers the necessary steps, including finding the gradient of the radius and using the negative reciprocal to determine the tangent's gradient. The video provides multiple examples with different coordinates and scenarios, such as using a variable in the equation. It also addresses potential exam questions, like finding the length and area related to the tangent. The tutorial emphasizes understanding the relationship between the radius and tangent, and how to apply these concepts in various contexts.

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

• Find the circle's radius.

• Calculate the circle's circumference.

• Draw a tangent line directly.

• Draw a line from the origin to the point on the circle.

How do you find the gradient of the line from the origin to point P?

• By measuring the angle.

• By calculating the circle's diameter.

• By using the coordinates of the point P.

• By using the circle's equation.

What is the relationship between the gradients of a radius and a tangent?

• They are both zero.

• They are negative reciprocals.

• They are both positive.

• They are equal.

In Example 1, what is the gradient of the tangent line?

• -1/4

• 1/4

• 4

• -4

What is the general form of the equation of a line?

• y = cx + m

• x = cy + m

• x = my + c

• y = mx + c

In Example 2, what is the gradient of the tangent line?

• 3/4

• -3/4

• -4/3

• 4/3

How do you express the equation of a tangent in the form ax + by = c?

• By subtracting the x coordinate from the y coordinate.

• By adding the x and y coordinates.

• By dividing the equation by the gradient.

• By multiplying through by the denominator of the fractions.

In Example 3, what is the value of K when K > 0?

• -6

• 5

• 6

• -5

What is the gradient of the tangent line in Example 3?

• -6/5

• 6/5

• -5/6

• 5/6

In Example 4, what are the coordinates of point A?

• (0, 26)

• (26, 0)

• (0, 39)

• (39, 0)