Coordinate geometry: circles

WMA12Topic 2.33 questions

Equations of circles and their properties, tangents and chords.

Specification points

Specification points for this topic are coming soon.

Get a plain-language explanation, a worked example and the usual mistake.

Sign in to get a plain-language explanation of any specification point.

Original practice questions written in the style of the exam.

Question 15 marks
The circle $C$ has centre $(2, -1)$ and passes through the point $P(5, 3)$ .

(a) Find an equation for $C$ .

(b) Find an equation of the tangent to $C$ at $P$ , giving your answer in the form $ax + by + c = 0$ , where $a$ , and are integers.
Mark scheme
- M1 Finds $r^2 = (5 - 2)^2 + (3 + 1)^2$ (1)
Question 24 marks
The line $y = x + k$ , where $k$ is a constant, is a tangent to the circle $x^2 + y^2 = 8$ .

b

b

c

1

)2

A1

(x - 2)^2 + (y + 1)^2 = 25

(1)

M1 Gradient of radius

= \dfrac{3 - (-1)}{5 - 2} = \tfrac{4}{3}

(1)

M1 Uses perpendicular gradient

-\tfrac{3}{4}

through

(5, 3)

(1)

A1

3x + 4y - 27 = 0

(1)

+

y2=

8

Find the possible values of $k$ .

Mark scheme

−

8)=

0