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 distance between the parallel lines $3x - 4y + 7 = 0$ and $3x - 4y + 5 = 0$ is
2. The ratio in which the YZ-plane divides the line segment formed by joining the points $(-2, 4, 7)$ and $(3, -5, 8)$ is
3. The radius of the circle $x^2 + y^2 - 4x - 8y - 45 = 0$ is
4. The focus of the parabola $x^2 = -16y$ is
5. The length of the major axis of the ellipse $16x^2 + 25y^2 = 400$ is
6. Find the equation of the line perpendicular to the line $x - 2y + 3 = 0$ and passing through the point $(1, -2)$.
7. Find the coordinates of the centroid of the triangle with vertices $(3, -5, 7)$, $(-1, 7, -6)$ and $(1, 1, 2)$.
8. Find the equation of the hyperbola with vertices $(\pm 2, 0)$ and foci $(\pm 3, 0)$.
9. Reduce the equation $\sqrt{3}x + y - 8 = 0$ into normal form. Find the values of $p$ and $\omega$.
10. Find the equation of the circle passing through the points $(4, 1)$ and $(6, 5)$ and whose center is on the line $4x + y = 16$.
11. Find the image of the point $(3, 8)$ with respect to the line $x + 3y = 7$ assuming the line to be a plane mirror.
12. Case Study: 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.
    (i) Let the ends be A on x-axis and B on y-axis. What is the relation between coordinates of A and B?
    (ii) Find the coordinates of P in terms of parameters.
    (iii) Find the equation of the locus of P.