JEE Questions for Maths Rectangular Cartesian Coordinates Quiz 8

If P = (1,, Q = (–1,and R = (2,are three given points, then the locus of a point S satisfying the relation SQ² + SR² = 2SP² is

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A straight line parallel to x-axis
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A circle through origin
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A circle with centre at the origin
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A straight line parallel to y-axis

The co-ordinates of the points O,A and B are (0,, (0,4), and (6,respectively. If a points P moves such that the area of ∆POA is always . Twice the area of ∆POB , then the equation to both parts of the locus of P is

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(x – 3y) (x + 3y) = 0
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(x – 3y) (x + y) = 0
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(3x – y) (3x + y) = 0
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None of these

A point P moves so that its distance from the point (a,is always equal to its distance form the line x + a = 0. The locus of the point is

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y2 = 4ax
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x2 = 4ay
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y2 + 4ax = 0
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x2 + 4ay = 0

The equation to the locus of a point which moves so that its distance from x-axis is always one half its distance from the origin, is

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2)
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O is the origin and A is the point (3,4). If a point P moves so that the line segment OP is always parallel to the line segment OA, then the equation to the locus of P is

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4x – 3y = 0
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4x + 3y = 0
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3x + 4y = 0
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3x – 4y = 0

The co-ordinates of the points A and B are (a,and (-a,respectively. If a point P moves so that PA² – PB² = 2k², when k is constant, then the equation to the locus of the point P, is

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2ax – k2 = 0
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2ax + k2 = 0
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2ay – k2 = 0
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2ay + k2 = 0

The transformed equation of 3x² + 3y² + 2xy = 2, when the co-ordinate axes are rotated through an angle of 45^o , is

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2)
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The locus of a point which moves in such a way that its distance from (0,is three times its distance from the x-axis , as given by

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2)
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The locus of a point whose distance from the point (–g, –f) is always \'a\' , will be,(where k = g² + f² – a² )

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2)
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None of the above

The locus of the moving point P, Such that 2PA = 3PB where A is (0,and B is (4, -is

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2)
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A point moves in such a way that its distance from (1, –is always the twice from (–3,5), then locus of the point is

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2)
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None of these

Let P be the point (1,and Q a point on the curve y² = 8x. The locus of mid point of PQ is

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2)
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if A(-a,and B(a,are two fixed points, then the locus of the point on which the line AB subtends the right angle, is

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2)
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The locus of P such that area of ∆PAB = 12 sq. units , where A (2,and B (–4,is

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(x + 3y –(x + 3y –= 0
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(x + 3y +(x + 3y –= 0
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(3x + y –(3x + y –= 0
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(3x + y +(3x + y += 0

Maths-Rectangular Cartesian Coordinates-46929.png

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2)
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None of these

If sum of distances of a point from the origin and lines x = 2 is 4 , then its locus is

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x2 – 12y = 36
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y2 + 12x = 36
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y2 – 12x = 36
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x2 + 12y = 36

Locus of centroid of the triangle whose vertices are (a cos t, a sin t), (b sin t, -b cos t) and (1,0), where t is a parameter; is

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2)
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If the distance of any point P from the point A (a + b, a – b) and B(a – b, a + b) are equal , then the locus of P is

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x – y = 0
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ax + by = 0
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bx – ay = 0
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x + y = 0

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

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2)
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Point of intersection of the diagonals of square is at origin and co-ordinate axis are drawn along the diagonals. If the side is of length a, then one which is not the vertex of square is

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2)
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If co-ordinates of the points A and B are (2,and (4,respectively and point M is such that A – M – B also AB = 3 AM, then the coordinates of M are

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2)
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The following points A(2a, 4a), B(2a, 6a) and C(2a + √3a,5a) (a >are the vertices of

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An acute angled triangle
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A right-angled triangle
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An isosceles triangle
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None of these

If the co-ordinates of the vertices of a triangle be (1,a),(2,b) and (c², 3), then the centroid of the triangle

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Lies at the origin
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cannot lie on x-axis
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cannot lie on y-axis
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None of these

Maths-Rectangular Cartesian Coordinates-46958.png

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3y + x = 20xy
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y + 3x = 20xy
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x + y = 20xy
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3x + 3y = 20xy

If the middle points of the sides of a triangle be (-2,3), (4,-and (4,5), then the centroid of the triangle is

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2)
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Maths-Rectangular Cartesian Coordinates-46965.png

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2)
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None of these

The ends of a rod of length l move on two mutually perpendicular lines. The locus of the point on the rod which divides it in the ratio 1 : 2 is

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2)
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None of these

Let A (2,-and B (-2,be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line

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3x – 2y = 3
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2x – 3y = 7
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3x + 2y = 5
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2x + 3y = 9

Let O(0,, P(3,, Q(6,be the vertices of the triangle OPQ . The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of the equal area. The co-ordinates of R are

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2)
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If the vertices P,Q,R of a triangle PQR are rational points, which of the following points of the triangle PQR is (are) always rational points (s)
(A rational point a point both of whose co-ordinates are rational numbers)

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Centroid
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Incentre
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Circumcentre
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Orthocentre
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All (1), (and (4)

JEE Questions for Maths Rectangular Cartesian Coordinates Quiz 8 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Rectangular Cartesian Coordinates Quiz 8 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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