The equations of the transverse and conjugate axes of a hyperbola respectively are x + 2 y - 3 = 0, 2 x - y + 4 = 0 and their respective length are √2 and 2/√3. The equation of the hyperbola is.
2/5 ( x + 2 y - 3)2 - 3/5 (2 x - y + 4)2 = 1
2/5 (2 x - y + 4)2 - 3/5 (x + 2 y - 3)2 = 1
2 (2 x - y + 4 )2 - 3 (x + 2 y - 3)2 = 1
2 (x + 2 y - 3)2 - 3 (2 x - y + 4)2 = 1
If 1, a1 , a2 , a3 . . . an-1 are the nth roots of unity , then the value of (1 - a1) (1 - a2) (1 - a3) . . . (1 - an-1) is
0
1
n
-n
If conjugate and reciprocal of a complex number z = x + iy are equal , then
x + y = 1
x2 + y2 = 1
x = 1 and y = 0
x = 0 and y = 1
a = 0 and b = 1
a = 1 and b = 0
a = 2 and b = -1
a = -1 and b = 2
If the complex numbers z1,z2 and z3 represent the vertices of an equilateral triangle such that | z1 | = | z2 | = | z3 | , then the sum of z1,z2 and z3 is
-1
2
If we express ( 2 + 3 i ) 2 in the form of ( x + iy ) , we get
-5 + 12 i
12 - 5 i
5 - 12 i
12 + 5 i
If -i + 3 is a root of x2 - 6x + k = 0 then the value of k is
√5
√10
10
If P is a multiple of n , then the sum of Pth power of nth roots of unity is
p
None of these
The polar form of complex number 1 + i is
√2 (cos π/4 + i sin π/4 )
√2 (cos 2π/4 + i sin 2π/4
√2 (cos π/4 - i sin π/4 )
√3 (sin 2π/4 + i cos 2π/4)
The solution of the equation | z | - z = 1 + 2i is
2 - 3/2 i
3/2 + 2i
3/2 - 2i
-2 + 3/2 i