1
The vertices of a triangle are (pq, 1/(pq)), (qr, 1/(qr)) and (rq, 1/(rp)) where p, q, r are the roo ...
2
A square of side a lies above the x-axis and has one vertex at the origin. The side passing through ...
3
Vertices of a variable triangle are (3, 4), (5 cos θ, 5 sin θ) and (5 sin θ,-5 cos θ), where θ ∈ R. ...
4
The line x/3 + y/4 = 1 meets the y-axis and x-axis at A and B, respectively. A square ABCD is constr ...
5
A line 'L' is drawn from P(4, 3) to meet the lines L1 and L2 given by 3x + 4y + 5 = 0 and 3x + 4y + ...
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In a triangle ABC if A = (1, 2) and internal angle bisectors through B and C are y=x and y=-2x, then ...
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Two sides of a triangle are along the coordinate axes and the medians through the vertices (other th ...
8
A rectangular billiard table has vertices at P (0, 0), Q (0, 7), R (10, 7) and S (10, 0). A small bi ...
9
In △ABC the coordinates of the vertex A are (4,-1) and lines x-y-1=0 and 2x-y=3 are internal bisecto ...
10
The area enclosed by 2|x |+ 3|y| ≤ 6 is ...
11
The lines y = mx, y intercepts on line x + y = 1, then mx make equal ...
12
The condition on a and b, such that the portion of the line ax + by - 1=0, intercepted between the l ...
13
The area of the triangle formed by the lines y = ax, x + y - a = 0 and the y-axis is equal to ...
14
Consider points A(3, 4) and B(7, 13). If P be a point on the line y = x such that PA + PB is minimum ...
15
If the straight lines 2x + 3y - 1 = 0, x + 2y - 1 = 0 and ax + by - 1 = 0 form a triangle with origi ...
16
A light ray emerging from the point source placed at P(2, 3) is reflected at a point 'Q' on the y-ax ...
17
Let O be the origin. If A(1, 0) and B(0, 1) and P(x, y) are points such that xy > 0 and x + y < 1, t ...
18
The graph y + 2xy + 40|x| =400 divides the plane into regions. Then the area of bounded region is ...
19
P, Q, R and S are the points of intersection with the coordinate axes of the lines px+qy=pq and qx+p ...
20
If sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is ...
21
If two vertices of a triangle are (-2, 3) and (5,-1), orthocentre lies at the origin and centroid on ...
22
If u = a1x + b1y + c1 = 0, v = a2x + b2y + c2 = 0 and a1 / a2 =b2/b2=c1/c2, then the curve u + kv = ...
23
The point A (2, 1) is translated parallel to the line x - y = 3 by a distance 4 units. If the new po ...
24
A rectangle ABCD has its side AB parallel to line y = x and vertices A, B and D lie on y = 1, x = 2 ...
25
Consider the points A(0, 1) and B(2, 0), and P be a point on the line 4x + 3y + 9 = 0. Coordinates o ...
26
A straight line passing through P(3, 1) meets the coordinate axes at A and B. It is given that dista ...
27
In a triangle ABC, A = (α, β), B = (2, 3) and C = (1, 3) and point A lies on line y = 2x + 3 where α ...
28
If a / bc-2 =( b/c)^.5 +(c/b)^.5, where a, b, c > 0, then family of lines vax + √by + vc =0 passes t ...
29
One of the diagonals of a square is the portion of the line x/2 + y/3=2 intercepted between the axes ...
30
Distance of origin from line (1+√3)y+(1-√3)x=10 along the line y=√3x+k is ...
31
The area of a parallelogram formed by the lines ax +- by +- c = 0 is ...
32
The straight line ax + by + c = 0 where abc ≠ 0 will pass through the first quadrant if ...
33
OPQR is a square and M, N are the middle points of the sides PQ and QR, respectively, then the ratio ...
34
One diagonal of a square is along the line 8x - 15y = 0 and one of its vertex is (1, 2). Then the eq ...
35
An equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest ...
36
A line of fixed length 2 units moves so that its ends are on the positive x-axis and that part of th ...
37
P(m, n) (where m, n are natural numbers) is any point in the interior of the quadrilateral formed by ...
38
In a triangle ABC, the bisectors of angles B and C lie along the lines y=x and y=0. If A is (1, 2), ...
39
If the vertices of a triangle are (√5, 0), (√3, √2) and (2, 1), then the orthocentre of the triangle ...
