Circles

Question 1

The equation of a circle with centre (𝑎,𝑏) and radius 𝑟 is?

Answer 1

(𝑥−𝑎)² + (𝑦−𝑏)² = 𝑟²

Question 2

If a line ’touches’ the circle, how many times does it intersect?

Answer 2

Intersects 1 time

Question 3

How do you find how many points of intersection there are between a straight line and a circle?

Answer 3

Find hybrid equation

𝑏²−4𝑎𝑐>0 means the line crosses the circle at two points

𝑏²−4𝑎𝑐=0 means the line touches the circle at exactly one point

𝑏2²−4𝑎𝑐<0 means the line does not intersect the circle at all

Question 4

What is a tangent to a circle and what is it compared to the radius?

Answer 4

A tangent to a circle is a straight line that touches the circle at exactly one point. The tangent is always perpendicular to the radius of the circle at the point of intersection.

Question 5

How would you find the equation of a tangent to a circle?

Answer 5

1. Find the gradient of the radius
2. Find the gradient of the tangent using m𝑟𝑎𝑑 × m𝑡𝑎𝑛= −1
3. Use 𝑦−𝑦₁ = m𝑡𝑎𝑛(𝑥−𝑥₁), using the points on the circumference

Question 6

What is a chord?

Answer 6

A chord is a straight line that connects any two points on the circumference of a circle. The longest chord of a circle is called the diameter.

Question 7

The perpendicular bisector of any chord will always pass through …

Answer 7

The perpendicular bisector of any chord will always pass through the centre of the circle.