JEE Questions for Maths Rectangular Cartesian Coordinates Quiz 4 - MCQExams.com

The locus of a point which moves such that the sum of the squares of its distance from three vertices of the triangle is constant, is a/an
  • circle
  • straight line
  • ellipse
  • None of these
If the sum of the distances from two perpendicular lines in a plane is 1, then its locus is
  • a square
  • a circle
  • a straight line
  • two intersecting lines
The orthocentre of triangle formed by lines 4x – 7y + 10 = 0, x + y = 5 and 7x + 4y = 15 is
  • (1,2)
  • (1,–2)
  • (–1, –2)
  • (–1,2)
The transformed equation of 3x2 + 3y2 + 2xy = 2, when the coordinate axes are rotated through an angle of 45o, is
  • x2 + 2y2 = 1
  • x2 + 2y2 = 1
  • 2x2 + y2 = 1
  • x2 + y2 = 1
  • x2 + 3y2 = 1
The locus of a point P which moves such that 2PA = 3PB where A(0,and B(4, -are points, is
  • 5x2 - 5y2 - 72x + 54y + 225 = 0
  • 5x2 + 5y2 - 72x + 54y + 225 = 0
  • 5x2 + 5y2 + 72x - 54y + 225 = 0
  • 5x2 + 5y2 - 72x - 54y - 225 = 0
The pair of lines √3x2 - 4xy + √3 y2 = 0 are rotated about the origin by π/6 in the anti - clock wise sense. The equation of the pair in the new position is
  • √3 y2 - xy = 0
  • √3 x2 - xy = 0
  • x2 - y2 = 0
  • √3 x2 + xy = 0
Let A (2, -and B (- 2,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
  • 2x + 3y = 9
  • 2x - 3y = 7
  • 3x + 2y = 5
  • 3x - 2y = 3
What is the equation of the locus of a point which moves such that 4 times its distance from the X-axis is the square of its distance from the origin?
  • x2 - y2 - 4y = 0
  • x2 + y2 - 4|y| = 0
  • x2 + y2 - 4x = 0
  • x2 + y2 - 4|x| = 0
The transformed equation of x2 + 6xy + 8y2 = 10 when the axes are rotated through an angle π/4 is
  • 15x2 - 14xy + 3y2 = 20
  • 15x2 + 14xy - 3y2 = 20
  • 15x2 + 14xy + 3y2 = 20
  • 15x2 - 14xy - 3y2 = 20
If P be the point (1,and Q be the point on y2 = 8x. Then, the locus of mid-point of PQ is
  • x2 - 4y + 2 = 0
  • x2 + 4y + 2 = 0
  • y2 + 4x + 2 = 0
  • y2 - 4x + 2 = 0
If the distance of any point P from the points A( a + b, a - b) and B(a - b ,a + b) are equal, then the locus of P is
  • ax + by = 0
  • x - y = 0
  • x + y = 0
  • bx - ay = 0
The co-ordinates of a point are (0,and the ordinate of another points is -3. If the distance between the two points is 5, then the abscissa of another point is
  • 3
  • –3
  • ± 3
  • 1
One of the vertices of a square is origin and adjacent sides of the square are coincident with positive axes.If side is 5 then which will not be its one of the vertex.
  • (0,5)
  • (5,0)
  • (–5, –5)
  • (0,0)
The straight line x + y = 0, 3x + y – 4 = 0 and x + 3y – 4 = 0 form a triangle which is
  • Right angled
  • Equilateral
  • Isosceles
  • None of these
If the distance between the points (a,and (3,be 8, then a =

  • Maths-Rectangular Cartesian Coordinates-46660.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-46661.png

  • Maths-Rectangular Cartesian Coordinates-46662.png

  • Maths-Rectangular Cartesian Coordinates-46663.png
The point whose abscissa is equal to its ordinate and which is equidistant from the points (1,and (0,is
  • (1,1)
  • (2,2)
  • (3,3)
  • (4,4)
A point equidistant from the point (2,and (0,is
  • (1,4)
  • (2,1)
  • (1,2)
  • (2,2)
The length of altitude through A of the triangle ABC, where A ≡ (–3,; B ≡ (4,–; C ≡ (5,, is

  • Maths-Rectangular Cartesian Coordinates-46667.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-46668.png

  • Maths-Rectangular Cartesian Coordinates-46669.png

  • Maths-Rectangular Cartesian Coordinates-46670.png
The distance of the middle point of the line joining the points (a sin θ,and (0, a cos θ) from the origin is

  • Maths-Rectangular Cartesian Coordinates-46672.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-46673.png
  • a (sin θ + cos θ)
  • a
The distance between the points (-115,and (100,is
  • – 215
  • – 15
  • 15
  • 215
The ratio in which x-axis divides the join of the points (2,-and (5,is
  • 2 : 1
  • 1 : 2
  • 2 : –1
  • None of these
The points which trisect the segment joining the points (0,and (9,are
  • (3,4), (6,8)
  • (4,3), (6,8)
  • (4,3), (8,6)
  • (3,4), (8,6)
The line x + y = 4 divides the line joining the points (-1,and (5,in the ratio
  • 2 : 1
  • 1 : 2
  • 1 : 2 externally
  • None of these
Three vertices of a parallelogram taken in order are (–1 , –, (2,–and (7,. The fourth vertex is
  • (1,4)
  • (4,1)
  • (1,1)
  • (4,4)
The points (1,2), (2,and (3,form the vertices of a triangle . The centroid of the triangle has co-ordinates
  • (4,5)
  • (3,2)
  • (2,3)
  • (6,9)
If the point (a,a) are placed in between the lines |x + y| = 4, then
  • |a| = 2
  • |a| = 3
  • |a| < 2
  • |a| < 2
The line joining points (2,–and (–5,is divided by y-axis in the ratio
  • 2 : 5
  • 2 : 3
  • 3 : 5
  • 1 : 2
If P(1,, Q(4,, R(5,and S(a,b) are the vertices of a parallelogram PQRS , then
  • a = 2,b = 4
  • a = 3,b = 4
  • a = 2,b = 3
  • a = 3,b = 5
The triangle joining the points P(2,7), Q(4,–1), R(–2,is
  • Equilateral triangle
  • Right-angled triangle
  • Isosceles triangle
  • Scalene triangles

Maths-Rectangular Cartesian Coordinates-46685.png
  • An equilateral triangle
  • An isosceles triangle
  • A right-angled triangle
  • None of these
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