10 questions🇬🇧English
⭕ Equations of Circles – A-level
Maths · A-level — practise centre-radius form, completing the square, tangents, chords and line–circle intersections.
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Questions
What are the centre and radius of the circle (x − 3)² + (y + 2)² = 25?
Centre (−3, 2), radius 5
Centre (3, −2), radius 25
Centre (−3, 2), radius 25
Centre (3, −2), radius 5
20s
Which is the equation of the circle with centre (−1, 4) and radius 3?
(x + 1)² + (y − 4)² = 3
(x + 1)² + (y − 4)² = 9
(x − 1)² + (y + 4)² = 9
(x − 1)² + (y + 4)² = 3
20s
AB is a diameter of a circle and C is another point on the circle. What is the size of angle ACB?
45°
60°
90°
180°
20s
By completing the square, find the centre and radius of x² + y² − 6x + 8y = 0.
Centre (3, −4), radius 5
Centre (3, −4), radius 25
Centre (−6, 8), radius 10
Centre (−3, 4), radius 5
30s
Where does the point (5, 1) lie relative to the circle (x − 2)² + (y + 3)² = 20?
At the centre of the circle
Inside the circle
On the circle
Outside the circle
30s
A circle has centre (2, 1) and the point P(5, 3) lies on it. What is the gradient of the tangent at P?
2/3
−2/3
3/2
−3/2
30s
A circle passes through the points (1, 2) and (5, 2). On which line must its centre lie?
x = 6
y = 2
y = 3
x = 3
30s
The line y = x + k is a tangent to the circle x² + y² = 8. What are the possible values of k?
k = ±2
k = ±8
k = ±4
k = ±2√2
60s
After substituting y = x + 3 into (x − 1)² + y² = 4, what does the discriminant tell you?
It is zero, so the line is a tangent
It is negative, so the line meets the circle twice
It is positive, so the line meets the circle twice
It is negative, so the line misses the circle
60s
What is the equation of the tangent to the circle x² + y² = 25 at the point (3, 4)?
4x + 3y = 24
3x + 4y = 25
3x − 4y = −7
4x − 3y = 0
60s