JEE Main Mathematics - Coordinate Geometry I
Exam Duration: 60 Mins Total Questions : 30
The incentre fo the triangle whose vertices are (-36, 7), (20, 7) and (0, -8) is
- (a)
(-1, 0)
- (b)
(1, 0)
- (c)
\((\frac 1{2}, 1)\)
- (d)
None of these
If the two vertices of a triangle are (5, -1), and (-2, 3) and if its orthocentre lies at the origin, then the coordinates of the third vertex are
- (a)
(4, 7)
- (b)
(-4, 7)
- (c)
(4, 7)
- (d)
(-7, -4)
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
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 coordinates of the image point of (1, 1) in the line 2x+3y+5=0, are
- (a)
\((\frac {27}{13}, \frac {47}{13})\)
- (b)
\((\frac {-47}{13}, \frac {27}{13})\)
- (c)
\((\frac {-27}{13}, \frac {-47}{13})\)
- (d)
\((\frac {27}{13}, \frac {47}{13})\)
A line makes intercepts p and q on the coordinate axes and when the coordinate axes are rotated through a fixed angle in anticlockwise direction (keeping the origin fixed), the same line makes intercepts p' and q' on the new-axes. Then
- (a)
\(\cfrac { 1 }{ { p }^{ 2 } } +\cfrac { 1 }{ { q }^{ 2 } } =\cfrac { 1 }{ { p }'^{ 2 } } +\cfrac { 1 }{ { q' }^{ 2 } } \)
- (b)
\({ p }^{ 2 }+{ q }^{ 2 }={ p }'^{ 2 }+{ q' }^{ 2 }\)
- (c)
\({ p }^{ 2 }+{ q' }^{ 2 }={ p }'^{ 2 }+{ q }^{ 2 }\)
- (d)
NONE OF THESE
The coordinates of the four vertices of a quaddrilateral taken in order are (-2, 4), (-1, 2), (1, 2) and (2, 4). The equation of the line passing through the point (-1,2) and dividing the quadrilateral into two parts of equal areas is
- (a)
x+1=0
- (b)
x+y=1
- (c)
x-y+3=0
- (d)
NONE OF THESE
The maximum number of points with rational coordiantes on a circle whose centre is \((\sqrt { 3 } ,0)\) is
- (a)
one
- (b)
two
- (c)
four
- (d)
infintely many
If the line hx+ky=1 touches the circle x2+y2=a2, then locus of the points (h,k) is a circle of radius
- (a)
a
- (b)
h
- (c)
k
- (d)
\(\cfrac { 1 }{ a } \)
The number of the common tangent to the circle x2+y2=4 and x2+y2-6x-8y=24, is
- (a)
0
- (b)
1
- (c)
3
- (d)
4
The equation of the circle drawn on the common chord of the circle x2+y2+2x=0 and x2+y2+2y=0 as a diameter is
- (a)
x2+y2+x+y=0
- (b)
x2+y2-x-y=0
- (c)
x2+y2+x-y=0
- (d)
x2+y2-x+y=0
If the area of triangle formed by the points (2a, b) (a + b, 2 b + a) and (2 b,2 a) be \(\lambda \) then the area of the triangle whose vertices are (a + b, a - b), (3b - a, b + 3a) and (3a-b,3b-a) will be
- (a)
\(\frac { 3 }{ 2 } \lambda \)
- (b)
\(3\lambda \)
- (c)
\(4\lambda \)
- (d)
none of these
The image of P (a, b) on y = -' X is Q and the image of Q on the line y = X is R. Then the mid point of R is
- (a)
(a + b, b + a)
- (b)
\(\left( \frac { a+b }{ 2 } ,\frac { b+a }{ 2 } \right) \)
- (c)
(a-b,b+a)
- (d)
(0,0)
For all real values of a and b lines (2a + b)x + (a + 3b) y + (b - 3a) = 0 and m x + 2y + 6 = 0 are concurrent, then m is equal to
- (a)
-2
- (b)
-3
- (c)
-4
- (d)
-5
The line segment joining the points (1, 2) and (- 2,1) is divided by the line 3x + 4y = 7 in the ratio
- (a)
3 : 4
- (b)
4: 3
- (c)
9:4
- (d)
4:9
If \(p_{ 1 },p_{ 2 },p_{ 3 }\) the length perpendiculars from the points \((m_{ 2 },2m)(m^{ ' },m+m^{ ' })\) and \((m^{ 2 },2m^{ ' })\) respectively on the line
\(xcos\alpha +ysin\alpha +\frac { sin^{ 2 }\alpha }{ cos\alpha } =0,p_{ 1 },p_{ 2 },p_{ 3 }\)
- (a)
AP
- (b)
GP
- (c)
HP
- (d)
none of these
The straight line y = x - 2 rotates about a point where it cuts x-axis and becomes perpendicular on the straight line ax + by + c = 0, then its equation is
- (a)
ax + by + 2a=0
- (b)
ay - bx + 2b=0
- (c)
ax + by + 2b=0
- (d)
none of these
The algebraic sum of the perpendicular distances from A (a1 b1); B (a2, b2) and C (a3, b3) to a variable line is zero, then the line passes through
- (a)
the orthocentre of \(\Delta ABC\)
- (b)
the centroid of \(\Delta ABC\)
- (c)
the circumcentre of \(\Delta ABC\)
- (d)
none of these
The points (2,3), (0, 2), (4, 5) and (0, r ) are concyclic if the value of t is
- (a)
1
- (b)
2
- (c)
17
- (d)
3
If the coordinates of the vertices of a triangle are rational numbers, then which of the following points of the triangle will always have rational coordinates
- (a)
centroid
- (b)
incentre
- (c)
circumcentre
- (d)
orthocentre
If the equation of the locus of a point equidistant from the points \((a_{ 1 },b_{ 1 })\) and \((a_{ 2 },b_{ 2 })\)
(a1-a2)x+(bi-b2)y+r=-0
- (a)
\(\frac { 1 }{ 2 } ({ a }_{ 2 }^{ 2 }+{ b }_{ 2 }^{ 2 }-{ a }_{ 2 }^{ 1 }-{ b }_{ 1 }^{ 2 })\)
- (b)
\(({ a }_{ 2 }^{ 2 }+{ b }_{ 2 }^{ 2 }-{ a }_{ 2 }^{ 1 }-{ b }_{ 1 }^{ 2 })\qquad \)
- (c)
\(\frac { 1 }{ 2 } ({ a }_{ 2 }^{ 2 }+{ b }_{ 2 }^{ 2 }-{ a }_{ 2 }^{ 1 }-{ b }_{ 1 }^{ 2 })\qquad \)
- (d)
\(({ a }_{ 2 }^{ 2 }+{ b }_{ 2 }^{ 2 }-{ a }_{ 2 }^{ 1 }-{ b }_{ 1 }^{ 2 })\qquad \)