The points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10, are
1) (3, 1), (–7, 11) 2) (3, 1), (7, 11) 3) (–3, 1), (–7, 11) 4) (1, 3), (–7, 11)... View Article
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A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of this point is
1) 3x2 + 4y2 = 192 2) 4x2 + 3y2 = 192 3) x2 + y2 = 192 4) None... View Article
Locus of the points which are at equal distance from 3x + 4y – 11 = 0 and 12x + 5y + 2 = 0 and which is near the origin is
1) 21x – 77y + 153 = 0 2) 99x + 77y – 133 = 0 3) 7x – 11y... View Article
A point moves so that the square of its distance from the point (3, -2) is numerically equal to its distance from the line 5x – 12y = 13. The equation of the locus of the point is
1) 13x2 + 13y2 – 83x + 64y + 182 = 0 2) x2 + y2 – 11x + 16y... View Article
The triangle formed by the lines x + y – 4 = 0, 3x + y = 4, x + 3y = 4 is
1) Isosceles 2) Equilateral 3) Right angled 4) None of these Solution: Given x + y – 4 = 0... View Article
The area of the triangle bounded by the straight line ax + by + c = 0, (a, b, c ? 0) and the coordinate axes is
1) ½ |c2/ab| 2) ½ |a2/ab| 3) ½ |b2/ab| 4) 1 Solution: Given ax + by + c = 0... View Article
If (-2, 6) is the image of the point (4, 2) with respect to line L = 0, then L =
1) 3x – 2y + 5 2) 3x – 2y + 10 3) 2x + 3y – 5 4) 6x... View Article
Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a fixed angle keeping the origin fixed, the same line L has intercepts p and q, then
1) a2 + b2 = p2 + q2 2) 1/a2 + 1/b2 = 1/p2 + 1/q2 3) a2 + p2... View Article
The coordinates of the foot of the perpendicular drawn from the point (3, 4) on the line 2x + y – 7 = 0 is
1) (9/5, 17/5) 2) (1, 5) 3) (-5, 1) 4) (1, -5) Solution: Let (a, b) be the foot of... View Article
If A and B are two points on the line 3x + 4y + 15 = 0 such that OA = OB = 9 units, then the area of the triangle OAB is
1) 18 sq. units 2) 18√2 sq. units 3) 18/√2 sq. units 4) None of these Solution: The perpendicular distance... View Article
A straight line passes through a fixed point (h ,k). The locus of the foot of perpendicular on it drawn from the origin is
1) x2 + y2 – hx – ky = 0 2) x2 + y2 + hx + ky = 0... View Article
The coordinates of the foot of the perpendicular drawn from (2, 4) to the line x + y = 1 is
1) (1/3, 3/2) 2) (–1/2, 3/2) 3) (4/3, 1/2) 4) (3/4, -1/2) Solution: Let (a, b) be the foot of... View Article
The straight lines x + 2y – 9 = 0, 3x + 5y – 5 = 0 and ax + by – 1 = 0 are concurrent, if the straight line 35x – 22y + 1 = 0 passes through the point
1) (a, b) 2) (b, a) 3) (–a, –b) 4) None of these Solution: Given x + 2y – 9... View Article
The lines (p – q)x + (q – r)y + (r – p) = 0, (q – r)x + (r – p)y + (p – q) = 0, (r – p)x + (p – q)y + (q – r) = 0 are
1) parallel 2) perpendicular 3) concurrent 4) none of these Solution: Given lines are (p – q)x + (q –... View Article
The value of k such that the lines 2x – 3y + k = 0, 3x – 4y – 13 = 0 and 8x – 11y – 33 = 0 are concurrent, is
1) 20 2) -7 3) 7 4) -20 Solution: Given lines 2x – 3y + k = 0 …(i) 3x... View Article
If the lines ax + by + c = 0, bx + cy + a = 0 and cx + ay + b = 0 be concurrent, then
1) a3 + b3 + c3 + 3abc = 0 2) a3 + b3 + c3 – abc =0 3)... View Article
The angle between the lines x cos ? + y sin ? = a and x sin ? – y cos ? = a is
1) β – α 2) π + β – α 3) π/2 + β – α 4) π/2 – β... View Article
The equation of the bisector of the acute angle between the lines 3x – 4y + 7 = 0 and 12x + 5y – 2 = 0 is
1) 21x + 77y – 101 = 0 2) 11x – 3y + 9 = 0 3) 31x + 77y... View Article
If the line 2x + 3ay -1 = 0 and 3x + 4y + 1 = 0 are mutually perpendicular, then the value of a will be
1) 1/2 2) 2 3) -1/2 4) None of these Solution: Given 2x + 3ay -1 = 0 …(i) 3x... View Article
The line passing through the points (3, -4) and (-2, 6) and a line passing through (-3, 6) and (9, -18) are
1) Perpendicular 2) Parallel 3) Makes an angle 600 with each other 4) None of these Solution: Let a line... View Article
