1. The combined equation of the lines bisecting the angle between the coordinate axes is:
A) x^2 + y^2 = 0
B) x^2 - y^2 = 0
C) x^2 + 2xy + y^2 = 0
D) x^2 - 2xy - y^2 = 0
2. The joint equation of two lines through the origin and each of which making an angle of 45^0 with the Y-axis is
A) x^2 + y^2 = 0
B) x^2 - y^2 = 0
C) x^2 - 2y^2 = 0
D) x^2 + 2y^2 = 0
3. The equation 3x^2 + 2xy + 7y^2 = 0 reprsents two
A) real and distinct lines
B) real and coincident lines
C) imaginary lines
D) perpendicular lines
4. If one of the lines represented by kx^2 + 10xy + 8y^2 = 0 is perpendicular to the line 2x - y = 5, then the value of k is :
A) -3
B) + 3 or -3
C) 3
D) None of these
5. The joint equation of the pair of lines parallel to the line x = 5 at distance 6 is
x^2 - 12x + 11 = 0
x^2 - 10x - 11 = 0
y^2 - 10y - 11 = 0
x^2 + 10x - 11 = 0
1) The orthocentre of the triangle formed by the lines xy = 0 and x + y = 1 is
(0, 0)
(2, 4)
(1, 1)
(-1, 0)
2) The combined equation of the pair of lines through (3, -2) and parallel to the lines x^2 - 4xy + 3y^2 = 0 is
x^2 - 4xy + 3y^2 - 14x - 24y - 45 = 0
x^2 + 4xy + 3y^2 + 14x - 24y - 45 = 0
x^2 - 4xy + 3y^2 - 14x + 24y + 45 = 0
x^2 + 4xy - 3y^2 - 14x + 24y + 45 = 0
If the angle between two st. lines represented by 2x^2 + 5xy + 3y^2 + 7y + 4 = 0 is tan^ -1(m), then m equals:
1
7
1/5
7/5
If the slope of one of the lines given by kx^2 + 4xy - y^2 = 0 exceeds the slope of other by 8, then k =
-1
12
1
-12
If the lines x^2- y^2 - 2x + 2y = 0 and x + 2y + k = 0 are concurrent, then the value of k is :
-3
3
2
-2
If the slopes of the lines given by ax^2 + 2hxy + by^2 = 0 are in the ratio 1 : 3, then h^2 : ab =
1 : 3
1 : 1
4 : 3
3 : 4
The equation of the pair of lines through origin and pependicular to 2x^2 + 5xy + 2y^2 + 10x + 5y = 0 is
2x^2 - 5xy + 2y^2 = 0
2x^2 + 5xy + 2y^2 = 0
2x^2 + 3xy - 2y^2 = 0
-2x^2 - 5xy + 2y^2 = 0
If the equation hxy + gx + fy + c = 0 represents a pair of lines, then
fh = cg
h^2 = gh
fg = ch
fgh = c
If the lines represented by the equation ax^2 - bxy - y^2 = 0 make angles A and B with x-axis, then tan(A + B) =
b/(1 + a)
a/(1+b)
-b/(1+a)
-a/(1+b)
The angle between the pair of straight lines y^2 sin^2(A) - xy sin2A + x^2 [cos^2(A) - 1] = 0 is :
pi/4
pi/3
2.pi/4
pi/2