AQA A Level Maths: Pure复习笔记3.2.5 Radius & Tangent

Radius & Tangent

 

What is the relationship between tangents and radii?

  • A tangent is a line that touches a circle at a single point but doesn't cut across the circle

3.2.5-Tangent

  • A tangent to a circle is perpendicular to the radius of the circle at the point of intersection

 

3.2.5-Tangent-Radius

How can I find the equation of the tangent line to a circle at a given point?

3.2.5-Tangent-Radius-Illustr_1

  •  STEP 1: Find the gradient of the radius OP

 

3.2.5-Tangent-Radius-Illustr_2

  • STEP 2: Find the gradient of the tangent

3.2.5-Tangent-Radius-Illustr_3

  • STEP 3: The equation of the tangent is the equation of the line with that gradient that goes through point P (see Equation of a Straight Line)

Exam Tip

  • If you understand the formula in Step 2 above, you can find the gradient of the tangent without having to find the gradient of the radius first.

Worked Example

3.2.5-Radius-Tangent-Example

转载自savemyexams

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