Questions covered in Basic

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. The equation of the circle with centre at origin and radius 5 is
2. The focus of the parabola $y^2 = 12x$ is
3. The eccentricity $e$ of an ellipse is
4. The length of the transverse axis of the hyperbola $\frac{x^2}{16} - \frac{y^2}{9} = 1$ is
5. The centre of the circle $(x+5)^2 + (y-3)^2 = 36$ is
6. Find the equation of the parabola with focus $(2, 0)$ and directrix $x = -2$.
7. Find the coordinates of the foci of the ellipse $25x^2 + 9y^2 = 225$.
8. Find the radius of the circle $x^2 + y^2 + 8x + 10y - 8 = 0$.
9. Find the equation of the hyperbola with vertices $(\pm 2, 0)$ and foci $(\pm 3, 0)$.
10. Find the equation of the ellipse whose vertices are $(\pm 13, 0)$ and foci are $(\pm 5, 0)$.
11. Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $16x^2 + y^2 = 16$.
12. Case Study: A circle is represented by the equation $x^2 + y^2 - 6x + 4y - 12 = 0$.
    (i) Find the center of the circle.
    (ii) Find the radius of the circle.
    (iii) Determine whether the point $(-2, 1)$ lies inside, outside or on the circle.