x(a sin a -b sin ẞ) − y(a cos a − b cos ß) = ab sin(a – B).

6. (i.) x=a, 1⁄2 {√2√3+√3-1}, -{{√2√3−√3+1}, {{√−2√3-√3−1},

11.

− = {√−2√3+√3+1}; y = −a, 2{√2√3−√3+1}, -{{√2√3+No3 − 1},

12. √rg. sin 20, where = its distance from O makes with vertical.

2.

V. PURE MATHEMATICS (1).

Sides 7x+y= II, 3x−y+1 = 0, x+3y+7=0;

bisectors 99x+77y+71 = 0, 7x-91 = 37. 3. A straight line.

4. (i.) A circle; (ii.) an ellipse, parabola, or hyperbola according as the constant is >, =, or < the distance between the centres.

OS2

5. Two.

6. When the distance of the point from the origin >

BC

8. 8, 2√3.

9. A parabola.

ANSWERS.

JUNE, 1892.

II. ALGEBRA.

1. a-a3b+9ab5.

2. x3+p2x2+pqx+q2.

3. 2x2+3x-5; (2x+5) (2x-5)(x+1)(x − 1), (2x+5)(x − 1)(x2 − x − 3).

9. 9, 10, sum 460; 1 and 9. 10. 35, 56.