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Time allotted 1 hr
1. Find the equations of the two straight lines through (1, 2) forming the two
sides of a square of which 4x + 7y = 12 is a diagonal.
2. A triangle is given by its vertices: A(- 6, - 2); B(4, 8) and C(2, - 10). The
equation of the bisection of the angle A is 3. 2x2 – 5xy + 2y2 = 0 represents two sides of a triangle whose centroid is (1, 1).
The equation of the third side is :
4. Number of straight lines passing through P(1, 4), if the sum of its positive
intercepts on coordinate axes is 8. 5.
A triangle ABC is formed by the lines 2x-3y-6=0;3x-y+3=0and3x+4y-12=0.If
the points P(a,0) and Q (0, b) always lie on or inside the triangle ABC, then
find range of a and b
6. Find equation of internal bisector at A of triangle ABC whose sides are,
AB: 3 x - 4 y = 7, BC: x = 1 & CA: 5 y = 12 x + 6.
7. Equation of the bisector of the acute angle between the lines, 3x - 4y + 7 = 0
and 12x + 5y-2=0 is:
(A) 11x-3y+9=0 (B) 11x+3y-9=0 (C) 3x-11y+9=0 (D) none 8. The image of the pair of lines represented by ax2 + 2h xy + by2 = 0 by the line
mirror y = 0 is : 9. If the slope of one of the lines given by ax2 +2hxy+by2 =0 is k times the
2
other, then if pkh =ab(1+k)2 , find p
10. Chords of the curve 4x2 + y2 - x + 4y = 0 which subtend a right angle at the
origin pass through a fixed point whose co-ordinates are
11. If the straight lines joining the origin and the points of intersection of the curve
5x2 +12xy-6y2 +4x-2y+3=0andx+ky-1=0 are equally inclined to the coordinate axes then the value of k:
12. The equation to the locus of a point P which moves so that its distance from the
point (3, 0) is three times its distance from (0, 2).Comment on locus of point P
13. P is the point (–1, 2), a variable line through P cuts the x and y axes at A and B
respectively. Q is the point on AB such that PA, PQ, PB are in H.P. If the locus
of Q is the line y = ax. Find a

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