Key learning points

1. Using the gradient of the radius through a given point, you can find the equation of the tangent at this same point.
2. You have already proved that the tangent at any point on a circle is perpendicular to the radius at that point.
3. You have already proved that the product of the gradients of two perpendicular lines is -1
4. Using the gradient of the tangent and the coordinates of the point, you can find the equation of the tangent.

Keywords

• Gradient - The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction.

• Radius - The radius is any line segment that joins the centre of a circle to its edge.

• Tangent - A tangent of a circle is a line that intersects the circle exactly once.

Common misconception