In which quadrant, the following points lie?
(-4,1)

3

(a)

Find the new coordinates of point (3,-4), if the origin is shifted to (1,2) by a translation.

3

(a)

If the axes are shifted to the point (-2,3) without rotation, then transform the equation of line y+3x=2 into new axes.

3

(a)

A point moves, so that the sum of its distances from (ae,0) and (-ae,0) is 2a , prove that the equation to its locus is \(\frac { { X }^{ 2 } }{ { a }^{ 2 } } +\frac { { Y }^{ 2 } }{ { b }^{ 2 } } =1\) , where b²=a²(1-e²).

3

(a)

Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram.

3

(a)

Find the angle between the lines joining the points (0,0), (2,3), and the points (2,-2), (3,5).

3

(a)

If the angle between two lines is \(\frac { \pi }{ 4 } \) and slope of one of the lines is \(\frac { 1 }{ 2 } \), then find the slope of the other line. 

3

(a)

Check whether the points (1,-3),(5,2) and(9,5) are collinear or not

3

(a)

Find the new transformed equation of the pair of straight lines x² + 2xy - y²+x-2 = 0 when the origin is shifted to a point (-4, 1).

3

(a)

Find the equation of the straight line whose transformed equation is 3x + 2y - 5 = 0 after shifting the origin to (2, -1).

3

(a)

Find the transformed equation of the parabola y²=4ax if the origin is shifted to (-3, 2).

3

(a)

Find the equation of the straight line which makes angle of 15° with the positive direction of x-axis and which cuts an intercept of length 5 on the negative direction of y-axis.

3

(a)

Find the new coordinates of point (a, -a) if the origin is shifted to (b, -b) by a translation.

3

(a)

find the transformed equation of the circle x²+y² = 9 when the origin is shifted to (-1, -3).

3

(a)

Find the equation of the line passing through the intersection of the lines 2x - y + 3 = 0 and x + 2y + 1 = 0 and parallel to y-axis.

3

(a)