The equation of the locus of the point whose distance from y-axis is half the distance from origin is

(a)

x² + 3y² = 0

(b)

x²- 3y² = 0

(c)

3x²+ y² = 0

(d)

3x²- y² = 0

Which of the following equation is the locus of (at², 2at)

(a)

\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)

(b)

\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

(c)

x² + y² = a²

(d)

y² = 4ax

The slope of the line which makes an angle 45^o with the line 3x- y = -5 are:

(a)

1, -1

(b)

\(\frac{1}{2},-2\)

(c)

\(1,\frac{1}{2}\)

(d)

\(2,-\frac{1}{2}\)

Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 + 2\(\sqrt{2}\) is

(a)

x + y + 2 = 0

(b)

x + y - 2 = 0

(c)

\(x+y-\sqrt{2}=0\)

(d)

\(x+y+\sqrt{2}=0\)

The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3, 4) with coordinate axes are

(a)

5, -5

(b)

5, 5

(c)

5, 3

(d)

5, -4

The equation of the bisectors of the angle between the co-ordinate axes are ______________

(a)

x+y=0

(b)

x-y=0

(c)

x\(\pm\)y=0

(d)

x=0

The equation of a line which makes an angle of 135° with positive direction of x-axis and passes through the point (1, 1) is ______________

(a)

x+y=2

(b)

x-y=0

(c)

\(2\sqrt {2x}-\sqrt {2y}=0\)

(d)

x-3y=0

The equation of the straight line bisecting the line segment joining the points (2, 4) and (4, 2) and making an angle of 45^o with positive direction of x-axis is ______________

(a)

x + y = 6

(b)

x - y = 0

(c)

x - y = 6

(d)

x + y = 0

The equation of median from verten B of the triangle \(\triangle ABC\)  the co-ordinates of whose vertices are A(-1, 6)B(-3, -9)C(5, -8) ___________

(a)

29x + 4y + 5 = 0

(b)

8x - 5y - 21 = 0

(c)

13x + 14y + 47 = 0

(d)

x + y -7 = 0

The equation of the straight line which passes through the point (2, 4) and have intercept on the axes equal in magnitude but opposite in sign is ______________

(a)

x - y = 2

(b)

x - y + 2 = 0

(c)

x - y + 1 = 0

(d)

x - y - 1 = 0