The equation of the pair of straight lines parallel to x-axis and touching the circle x2 + y2- 6x - 4y -12 = 0 is
y2 - 4y - 21 = 0
y2 + 4y - 21 = 0
y2 - 4y + 21 = 0
y2 + 4y + 21 = 0
If the foot of the perpendicular from the origin to a straight line is at the point (3 - 4). Then, the equation of the line is
3x - 4y = 25
3x - 4y + 25 = 0
4x + 3y - 25 = 0
4x - 3y + 25 = 0
The angle between lines joining origin and intersection points of line 2x + y = 1 and curve 3x2 + 4yx - 4x + 1= 0 is
The equation of the bisector of the acute angle between the lines 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 is
99x - 27y - 81 = 0
11x - 3y + 9 = 0
21x + 77y - 101 = 0
21x + 77y + 101 = 0
The value of k so that x2 + y2 + kx + 4y + 2 = 0 and 2(x2 + y) - 4x - 3y + k = 0 cut orthogonally is
The two lines x = my + n, z = py + q and x = m'y + n', z =p'y + q' are perpendicular to each other, if
mm' + pp' = 1
mm' + pp' = - 1
The shortest distance between the lines and is
units
units
units
units
B.
units
Given, lines are and
The vector form of given equations are
and
On comparing these equations with
, we get
Now, (a2 - a1)
=
=
Then,