Rectangular Cartesian Coordinates Test

Result

Rectangular Cartesian Coordinates Test - 24

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Question 1
4 / -1

If P = (1,0) , Q = (–1,0) and R = (2,0) are three given points, then the locus of a point S satisfying the relation SQ² + SR² = 2SP² is

A
A straight line parallel to x-axis

B
A circle through origin

C
A circle with centre at the origin

D
A straight line parallel to y-axis

Solution
Question 2
4 / -1

The co-ordinates of the points O,A and B are (0,0) , (0,4), and (6,0) 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

A
(x – 3y) (x + 3y) = 0

B
(x – 3y) (x + y) = 0

C
(3x – y) (3x + y) = 0

D
None of these

Solution
Question 3
4 / -1

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

A
y² = 4ax

B
x² = 4ay

C
y² + 4ax = 0

D
x² + 4ay = 0

Solution
Question 4
4 / -1

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

A

B

C

D

Solution
Question 5
4 / -1

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

A
4x – 3y = 0

B
4x + 3y = 0

C
3x + 4y = 0

D
3x – 4y = 0

Solution
Question 6
4 / -1

The co-ordinates of the points A and B are (a,0) and (-a,0) 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

A
2ax – k² = 0

B
2ax + k² = 0

C
2ay – k² = 0

D
2ay + k² = 0

Solution
Question 7
4 / -1

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

A

B

C

D

Solution
Question 8
4 / -1

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

A

B

C

D

Solution
Question 9
4 / -1

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

A

B

C

D
None of the above
Question 10
4 / -1

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

A

B

C

D

Solution