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 slope of the line passing through the points $(3, -2)$ and $(-1, 4)$ is
2. The point $(-4, 2, -5)$ lies in which octant?
3. The radius of the circle $(x-2)^2 + (y+3)^2 = 25$ is
4. The length of the latus rectum of the parabola $y^2 = 12x$ is
5. The distance of the point $(3, -5)$ from the line $3x - 4y - 26 = 0$ is
6. Find the equation of the line passing through $(-4, 3)$ with slope $\frac{1}{2}$.
7. Find the coordinates of the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{9} = 1$.
8. Find the distance between the points $P(2, 3, 5)$ and $Q(4, 3, 1)$.
9. Find the equation of the line passing through the point $(2, 2)$ such that the sum of its intercepts on the axes is 9.
10. Find the equation of the hyperbola with vertices $(\pm 2, 0)$ and foci $(\pm 3, 0)$.
11. Find the coordinates of the foot of the perpendicular drawn from the origin to the line $3x + 4y - 25 = 0$.
12. Case Study: An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the center. The height of the arch changes as we move away from the center.
    (i) Find the equation of the ellipse (taking center as origin).
    (ii) Find the height of the arch at a point 2 m from the center.