Mathematics - Coordinate Geometry I
Exam Duration: 45 Mins Total Questions : 30
The coordinates of the middle points of the sides of a triangle are (4, 2), (3, 3) and (2, 2); then the coordinates of its centroid me
- (a)
\((3, \frac 7{3})\)
- (b)
(3,3)
- (c)
(4, 3)
- (d)
None of these
Area of the parallelogram formed by the lines y=mx, y=mx+1, y=nx, y=nx+1, is
- (a)
\(\frac { |m+n| }{ (m-n)^2 } \)
- (b)
\(\frac { 2 }{ (m+n) } \)
- (c)
\(\frac { 1 }{ (m+n) } \)
- (d)
\(\frac { 1 }{ (m-n) } \)
The equation to the locus of point which moves so that its distance from the point. (ak, 0) is k times its distance from the point. \((\frac a{k}, 0)\)is
- (a)
x2-y2=a2
- (b)
x2+y2=a2
- (c)
x2+y2=k2-a2
- (d)
x2-y2=a2-k2
The line (\(\lambda+2\mu)x + (\lambda-3\mu)y = \lambda - \mu,\)for different values of \(\lambda\) and \(\mu\) passes through the point
- (a)
\((\frac 3{5},\frac{2}{5})\)
- (b)
\((\frac 2{5},\frac{2}{5})\)
- (c)
\((\frac 3{5},\frac{3}{5})\)
- (d)
\((\frac 2{5},\frac{3}{5})\)
Two sides of an isosceles triangle are given by 7x+y+3=0 and x-y+3=0. The thrid side passes throguh the point (1, 0). The equation of the third side is
- (a)
3x+y-3=0
- (b)
x-y-1=0
- (c)
x-3y-1=0
- (d)
None of these
The lines represented by ax2+2hxy-ax2=0 are
- (a)
coicident
- (b)
perpendicular
- (c)
parallel
- (d)
NONE OF THESE
If the sum of slopes of the lines 3x2+2hxy-7y2=0, equals product of the slopes, then h=
- (a)
\(\cfrac { 1 }{ 2 } \)
- (b)
\(\cfrac { -1 }{ 2 } \)
- (c)
\(\cfrac { 3 }{ 2 } \)
- (d)
\(\cfrac { -3 }{ 2 } \)
The equation of the circles having radius as 5 units whose centre lies on the x-axis which passes through the point (2, 3), are
- (a)
x2+y2-12x+11=0
x2+y2+4x-21=0
- (b)
x2+y2-12x-11=0
x2+y2+4x+21=0
- (c)
x2+y2-12x+11=0
x2+y2+4x+21=0
- (d)
NONE OF THESE
The equation of the circle which passes through (1, 0), (0, 1) and has radius as small as possible.
- (a)
x2+y2-x-y=0
- (b)
x2+y2-x+y-2=0
- (c)
x2+y2+2x+2y-3=0
- (d)
NONE OF THESE
If lines 2x-3y=5 and 3x-4y=7 are dyameters of a circle of area 154 sq. units then the equation of the circle is
- (a)
x2+y2+2x-2y=62
- (b)
x2+y2+2x-2y=47
- (c)
x2+y2-2x+2y=47
- (d)
x2+y2-2x+2y=62
The angle between the tangents from the point (4,3) to the circle x2+y2-2x-4y=0 is
- (a)
300
- (b)
450
- (c)
600
- (d)
900
The tangents to the circle x2+y2=169 at the point (5,12) and (12, -5) are
- (a)
parallel
- (b)
perpendicular
- (c)
conicident
- (d)
NONE OF THESE
If the distance of any point (x, y) from the origin is defined as d (x, y) = max { I x I, Iy I}, d (x, y) = a, non zero constant, then the locus is
- (a)
a circle
- (b)
a straight line
- (c)
a square
- (d)
a triangle
A ray of light coming from the point (1, 2) is reflected at a point A on the x -axis and then passes through the point (5,3). The coordinates of the point A are
- (a)
\(\frac { 13 }{ 5 } ,0\)
- (b)
\(\frac { 5 }{ 13 } ,0\)
- (c)
(-7,0)
- (d)
none of these
Let n be the number of points having rational coordinates equidistant from the point (0,13), then
- (a)
\(n\le 1\)
- (b)
n = 1
- (c)
\(n\le 2\)
- (d)
n>2
If t1,t2 and t3 are distinct, the points (t1,2at1+a(t1) \(t_{ 2 }2at_{ 2 }+at_{ 2 })\) are collinear if
- (a)
\(t_{ 1 }t_{ 2 }t_{ 3 }=-1\)
- (b)
\(t_{ 1 }+t_{ 2 }+t_{ 3 }=-t_{ 1 }t_{ 2 }t_{ 3 }\)
- (c)
\(t_{ 1 }+t_{ 2 }+t_{ 3 }=0\)
- (d)
\(t_{ 1 }+t_{ 2 }+t_{ 3 }=-1\)
If each of the points (x,4), (- 2, YI) lies on the line joining the points (2, - 1), (5, - 3), then the point P (x1' Y1) lies on the line
- (a)
6(x+'y)-25=0
- (b)
2x+6y+1=0
- (c)
2x + 3y - 6 = 0
- (d)
6 (x + y) - 23 = 0
If the point P (x, y) be equidistant from the points A (0 + b, a - b) and B (a - b, a + b), then
- (a)
ax = by
- (b)
bx = ay
- (c)
X2 - y2 = 2 (ax + by)
- (d)
P can be (a, b)
Let \(L_{ 1 }\) = ax + by + a \(\sqrt [ 3 ]{ b } =0 \) and L2 == bx - ay + b \(\sqrt [ 3 ]{ a } =0\) be two straight lines. The equations of the bisectors of the angle formed by the loci. Whose equations are \(\lambda _{ 1 }L_{ 1 }-\lambda _{ 2 }L_{ 2 }=0\) and \(\lambda _{ 1 }L_{ 2 }-\lambda _{ 2 }L_{ 2 }=0\) \(\lambda _{ 1 } \) and \(\lambda _{ 2 }\) being non zero real numbers, are given by
- (a)
\(L_{ 1 }=0\)
- (b)
\(L_{ 2 }=0\)
- (c)
\(\lambda _{ 1 }L_{ 1 }-\lambda _{ 2 }L_{ 2 }=0\)
- (d)
\(\lambda _{ 1 }L_{ 2 }-\lambda _{ 2 }L_{ 2 }=0\)
Let A (2, - 3) and B (-2, 1) be vertices of a ABC. If the centroid of this triangle moves on the line 2x + 3y =-1 then the locus of the vertex C is the line
- (a)
2x + 3y = 9
- (b)
2x - 3y = 7
- (c)
3x + 2y =-S
- (d)
3x - 2y =-3