Equation of a Tangent
Maths: Edexcel A Level Pure Maths, topic 3.2.3
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):
Step 1
- First calculate the gradient of the line from the origin to (-3,4):
- Gradient of purple line is m = 4⁄-3
Step 2
- The tangent will be perpendicular to the purple line so the gradient of the tangent is -1⁄m:
- gradient of tangent = -1⁄m = 3⁄4
Step 3
- Substitute in (-3,4) to y = 3⁄4x + c:
- 4 = -9⁄4 + c
- c = 25⁄4
- So the equation of tangent is y = 3⁄4x + 25⁄4.
Test yourself on Equation of a Tangent
Circle 1 has the equation x² + y² = 25.
Circle 2 has the equation x² + y² = 100.
Which circle is larger and why?What is the radius of a circle with equation:
x² + y² = 49What is the radius of a circle with equation:
x² + y² = 16What are the coordinates of the centre of a circle with equation:
x² + y² = 16