Transformation of axes

The new coordinates of a point (4, 5), when the origin is shifted to the point (1,-2) are

• (3, 7)

• (3, 5)

• None of these

• (5, 3)

Without changing the direction of coordinate axes, origin is transferred to (h,k), so that the linear (one degree) terms in the equation x^2 + y^2 - 4x + 6y - 7 = 0 are eliminated. Then the point (h,k) is

• (-3, 2)

• (3, 2)

• None of these

• (2, -3)

The equation of the locus of a point whose distance from (a, 0) is equal to its distance from y-axis, is

• y^2 - 2ax + a^2 = 0

• y^2 - 2ax = a^2

• y^2 + 2ax = a^2

• y^2 + 2ax + a^2 = 0

Two points A and B have coordinates (1, 0) and (-1, 0) respectively and Q is a point which satisfies the relation AQ - BQ = ± 1. The locus of Q is

• 12x^2 - 4y^2 = 3

• 12x^2 + 4y^2 = 3

• 12x^2 - 4y^2 + 3 = 0

• 12x^2 + 4y^2 + 3 = 0

The locus of a point P which moves in such a way that the segment OP, where O is the origin, has slope √3 is

• √3x + y = 0

• √3x - y = 0

• x + √3y = 0

• x - √3y = 0

If the coordinates of a point be given by the equation x = a(1 - cosθ), y = a sinθ, then the locus of the point will be

• A parabola

• An ellipse

• A circle

• A straight line

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 SQ^2 + SR^2 = 2SP^2 is

• A circle with centre at the origin

• A circle through origin

• A straight line parallel to y-axis

• A straight line parallel to x-axis

The coordinates 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 ΔPOA is always twice the area of ΔPOB, then the equation to both parts of the locus of P is

• (x-3y)(x+3y) = 0

• None of these

• (x-3y)(x+y) = 0

• (3x-y)(3x+y) = 0

A point moves in such a way that the sum of square of its distance from the points A(2,0) and B(-2,0) is always equal to the square of the distance between A and B. The locus of the point is

• x^2 + y^2 + 4 = 0

• x^2 + y^2 - 4 = 0

• x^2 + y^2 - 2 = 0

• x^2 + y^2 + 2 = 0

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

• x^2 = 4ay

• y^2 = 4ax

• y^2 + 4ax = 0

• x^2 + 4ay = 0