2.6.2

Tangent on a Circle

Test yourself

Tangent of a Circle

A circle with centre (0,0) and radius r has the equation x2 + y2 = r2. Find the tangent to the circle x2 + y2 = 25 at the point (-3,4):

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Step 1

  • First calculate the gradient of the line from the origin to (-3,4):
    • Gradient of purple line is m = 4-3
Illustrative background for Step 2Illustrative background for Step 2 ?? "content

Step 2

  • The tangent will be perpendicular to the purple line so the gradient of the tangent is -1m:
    • gradient of tangent = -1m = 34
Illustrative background for Step 3Illustrative background for Step 3 ?? "content

Step 3

  • Substitute in (-3,4) to y = 34x + c:
    • 4 = -94 + c
    • c = 254
    • So the equation of tangent is y = 34x + 254.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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