One possible condition for the three points (a, b), (b, a) and (a2, - b2) to be collinear is
a - b = 2
a + b = 2
a = 1 + b
a = 1 - b
If the mth term and the nth term of an AP are respectively and , then the mnth term of the AP is
1
The function f(x) = satisfies the equation
f(x + 2) - 2f(x + 1) + f(x) = 0
f(x) + f(x + 1) = f{x(x + 1)}
f(x) + f(y) =
f(x + y) = f(x)f(y)
The value of (1 - w + w2)5 + (1 + w - w2)5, where w and w2 are the complex cube roots of unity, is
0
32w
- 32
32
The equation of the circle which passes through the points of intersection of the circles x2 + y2 - 6x = 0 and x2 + y2 - 6y = 0 and has its centre at , is
x2 + y2 + 3x + 3y + 9 = 0
x2 + y2 + 3x + 3y = 0
x2 + y2 - 3x - 3y = 0
x2 + y2 - 3x - 3y + 9 = 0
C.
x2 + y2 - 3x - 3y = 0
The equations of given circles are,
x2 + y2 - 6x = 0 ...(i)
x2 + y2 - 6y = 0 ...(ii)
On solving Eqs. (i) and (ii), we get
x = 0, y = 0 or x = 3, y = 3
Since, this circle passes through (0, 0), thus equation of circle becomes
x2 + y2 - 3x - 3y + c = 0
If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the ellipse is
If t is a parameter, then x = , y = represents
an ellipse
a circle
a pair of straight lines
a hyperbola