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Edexcel A Level Maths: Pure:復(fù)習(xí)筆記3.2.5 Radius & Tangent

Category: A-level課程, 國際課程, 教材筆記, 福利干貨 Date: 2022年10月27日 上午10:41

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

Tangent, A Level & AS Level Pure Maths Revision Notes

  • 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

 

 

 

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