GCSE Secondary Maths Age 13-17 - Graphs: Equation of a Tangent - Explained

The video tutorial covers solving a geometry problem involving a circle and a tangent line. It begins with sketching the circle and plotting a point on it. The instructor then explains how to find the equation of the tangent line at that point by calculating the gradient and intercept. The process involves understanding the relationship between the radius and the tangent, and using algebraic manipulation to derive the final equation. The tutorial emphasizes the importance of visual aids and methodical problem-solving.

What is the equation of the circle L?

• x^2 + y^2 = 16

• x^2 + y^2 = 8

• x^2 + y^2 = 2

• x^2 + y^2 = 4

What are the coordinates of point P on circle L?

• (3/2, root 7/2)

• (2, 2)

• (1, 1)

• (0, 0)

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

• y = mx + b

• y = mx + c

• y = m + cx

• y = mx^2 + c

How do you find the gradient of a line perpendicular to another?

• Flip the gradient and change its sign

• Double the gradient

• Add 1 to the gradient

• Square the gradient

What is the gradient of the radius OP?

• root 7/3

• 3/root 7

• 7/3

• 3/7

What is the gradient of the tangent line at point P?

• -root 7/3

• 3/root 7

• -3/root 7

• root 7/3

What is the final equation of the tangent line at point P?

• y = 3 root 7/7 x - 8 root 7/7

• y = -3 root 7/7 x - 8 root 7/7

• y = 3 root 7/7 x + 8 root 7/7

• y = -3 root 7/7 x + 8 root 7/7

What is the importance of the gradient of OP in solving the problem?

• It is used to find the center of the circle

• It gives the y-intercept of the tangent

• It determines the circle's radius

• It helps find the gradient of the tangent

What is the significance of the perpendicular relationship in this problem?

• It is used to find the circle's area

• It determines the circle's diameter

• It gives the equation of the circle

• It helps find the tangent's gradient

What is the key takeaway from solving this problem?

• Determining the length of a radius

• Understanding the connection between radius and tangent

• Learning to calculate circle area

• Finding the center of a circle