brodidit for students
Home / Practice / ECAT / Mathematics / Circles, parabolas, ellipses and hyperbolas
Circles, parabolas, ellipses and hyperbolas
5 ECAT Mathematics questions with answers and explanations.
Printable worksheet with answer key
-
What are the centre and radius of the circle x² + y² - 6x + 8y = 0?
- 1 Centre (-3, 4), radius 5
- 2 Centre (6, -8), radius 10
- 3 Centre (3, -4), radius 5
- 4 Centre (3, -4), radius 25
Show answer
Correct answer: Centre (3, -4), radius 5
Completing the square gives (x - 3)² + (y + 4)² = 25, so the centre is (3, -4) and the radius is 5.
-
What is the length of the major axis of the ellipse x² / 9 + y² / 4 = 1?
- 1 4
- 2 3
- 3 9
- 4 6
Show answer
Correct answer: 6
The larger denominator is 9, so a = 3 and the major axis has length 2a = 6.
-
What are the asymptotes of the hyperbola x² - y² = 1?
- 1 y = 0 and x = 0
- 2 y = x and y = -x
- 3 x = 1 and x = -1
- 4 y = 2x and y = -2x
Show answer
Correct answer: y = x and y = -x
For x² - y² = 1 the asymptotes come from x² - y² = 0, which gives y = x and y = -x.
-
What is the focus of the parabola x² = 12y?
- 1 (3, 0)
- 2 (12, 0)
- 3 (0, 3)
- 4 (0, 12)
Show answer
Correct answer: (0, 3)
Comparing with x² = 4ay gives 4a = 12, so a = 3 and the focus is (0, 3).
-
What is the eccentricity of a parabola?
- 1 Less than 1
- 2 0
- 3 1
- 4 Greater than 1
Show answer
Correct answer: 1
A parabola is defined by its distance to the focus equalling its distance to the directrix, so e = 1.