Shifting of Axes

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.

If the origin is shifted to the point (2, 3), the coordinates of a point become (5, -4). Find the original coordinates, when the axes are parallel.

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

Q. 10. The equation of the line segment AB is y = x. If A and B lie on the same side of the line mirror 2x y = 1, the image of AB has the equation 4)RBCs of human suffering from malaria

Q. Write the distance between the lines 4x + 3y − 11 = 0 and 8x + 6y − 15 = 0.

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

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

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. Determine the distance between the following pair of parallel lines:
(i) 4x − 3y − 9 = 0 and 4x − 3y − 24 = 0
(ii) 8x + 15y − 34 = 0 and 8x + 15y + 31 = 0
(iii) y = mx + c and y = mx + d
(iv) 4x + 3y − 11 = 0 and 8x + 6y = 15