10.

11.
12.

13.
14.

15.

16.

18.

19.

248530

2 D 30563
State Ceva’s theorem.
The triangle AABC has vertices A (1,3), B (-1, 0) and C (4,0) and the points 2 (0, 0), ९ (तं त

and R (= ने lie on BC, CA and AB respectively :

9

(a) Determine the ratios in which P, Q and R divide the sides of the triangle.
(b) Determine whether the lines AP, BQ and CR are concurrent.
Find the equation of the line that passes through the point [2, 5, 4] and [8, 1, 7].
Determine whether the points [1, 2, 3], [1, 1, -2] and [2, 1, -9] are collinear.
Section B

Answer any number of questions.
Each question carries 5 marks.
Ceiling is 30.

Derive the standard form of the equation of the hyperbola.
State and prove reflection property of the ellipse.

Show that a perpendicular from a focus of a parabola to a tangent meets the tangent on the
auxiliary circle of the parabola.

Determine the image of the line 3x — y + 1 5 0 under the affine transformation

3 WE
t(X)=|2 2 | +| 2 |,XeR”.
-1 2 4

Determine the affine transformation which maps the points (1, — 1), (2, — 2) and (3, — 4) to the
points (8, 13), (8, 4) and (0, — 1) respectively.

Prove that an affine transformation preserves ratios of length along parallel straight lines.

Determine the point of RIP? at which the line through the points [1, 2, —3] and [2, —1, 0] meets the
line through the points [1, 0, — 1] and [1, 1, 1].

248530