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

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 point on the line 2x- 3y = 5 is equidistance from (1, 2) and (3, 4) is

(a)

(7, 3)

(b)

(4, 1)

(c)

(1, -1)

(d)

(-2, 3)

The length of \(\bot\) from the origin to the line \(\frac{x}{3}-\frac{y}{4}=1,\) is 

(a)

\(\frac{11}{5}\)

(b)

\(\frac{5}{12}\)

(c)

\(\frac{12}{5}\)

(d)

\(\frac{-5}{12}\)

If one of the lines given by 6x² - xy + 4cy² = 0 is 3x + 4y = 0, then c equals to

(a)

-3

(b)

-1

(c)

3

(d)

1

The equation of the line passing through (1, 5) and perpendicular to the line 3x -5y + 7 = 0 is ______________

(a)

5x + 3y - 20 = 0

(b)

3x - 5y + 7 = 0

(c)

3x - 5y + 6 = 0

(d)

5x + 3y + 7 = 0

If 7x² - 8xy +A = 0 represents a pair of perpendicular lines, the A is ______________

(a)

7

(b)

-7

(c)

-8

(d)

8

Find the nearest point on the line 3x + y = 10 from the origin is ______________

(a)

(2, 1)

(b)

(1, 2)

(c)

(3, 1)

(d)

(1,3)

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 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