Questions covered in Standard

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 $(-3, 2)$ and radius 4 is
2. The length of the latus rectum of the hyperbola $16x^2 - 9y^2 = 144$ is
3. The eccentricity of the ellipse $9x^2 + 4y^2 = 36$ is
4. The focus of the parabola $x^2 = -16y$ is
5. If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ passes through the origin, then
6. Find the equation of the parabola with vertex at $(0, 0)$ and focus at $(0, 2)$.
7. Find the coordinates of the foci and the vertices of the ellipse $4x^2 + 9y^2 = 36$.
8. Find the equation of the hyperbola with vertices $(\pm 2, 0)$ and foci $(\pm 3, 0)$.
9. Find the equation of the circle passing through the points $(2, 3)$ and $(-1, 1)$ and whose centre is on the line $x - 3y - 11 = 0$.
10. Find the equation of the ellipse whose major axis is on the x-axis and passes through the points $(4, 3)$ and $(6, 2)$.
11. A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.
12. Case Study: A beam is supported at its ends by supports which are 12 metres apart. Since the load is concentrated at its center, there is a deflection of 3 cm at the center and the deflected beam is in the shape of a parabola.
    (i) Find the equation of the parabola (take vertex at origin).
    (ii) How far from the center is the deflection 1 cm?
    (iii) What is the deflection at a distance of 6 m from the center?