Shifting of Axes

Q.

In the new coordinate system origin is shifted to (h, k) and the axes are rotated through angle of ${90}^{\circ }$ in the anti-clockwise direction. The new co-ordinates of (x, y) is obtained by the following method.

1) (x + iy) becomes (x + iy) $e^{\frac{-i\pi }{2}}$

Let it be (x+iy) or (x, y)

2)(x, y) becomes (x - h, y - k)

1. True

2. False

Q.

If origin is shifted to the point (h, k) the new coordinate of (x, y) will be (x+h, y+k)

1. True

2. False

Q.

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

1. (3, 2)

2. (- 3, 2)

3. (2, - 3)

4. None of these

Q.

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

1. (3, 7)

2. None of these

3. (3, 5)

4. (5, 3)

Q. Equation of the image of the pair of rays y = | x | by the line x = 1 is

1. | y | + 2 = x
2. none of these
3. y = | x - 2|
4. | y | = x + 2

Q.

If origin is shifted to the point $(2,3)$ without rotation of axes then the coordinates of the point $P$ which divides the join of $A(4,8)$ and $B(7,14)$ in the ratio $1:2$ or $2:1$ with respect to the new system of coordinates can be

1. $(2,5)$

2. $(3,7)$

3. $(4,9)$

4. $(5,11)$

Q. The area of a triangle remains unchanged when the origin is shifted to (h, k).

1. True
2. False

Q. If the origin is shifted to (7, -4), then the coordinates of the point P(4, 5) will become .

1. (-3, 9)
2. (-3, -9)
3. (3, 9)
4. (3, -9)

Q. The point where the origin has to be shifted so that the equation $y^2+4y+8x-2=0$ will not contain $y$ and the constant term is

1. $(\frac{3}{4},-2)$
2. $(\frac{3}{5},-2)$
3. $(2,4)$
4. $(1,-4)$

Q. The transformed equation of $x^2+2y^2+2x-4y+2=0$ when origin is shifted to the point $(-1,1)$ with out rotation of axes, is

1. $X^2-2Y^2=1$
2. $2X^2+Y^2=1$
3. $X^2+2Y^2=1$
4. $X^2-Y^2=0$