If f(x) = 2100x + 1, g(x) = 3100x + 1, then the set ofreal numbers x such that f{g(x)} = x is
empty
a singleton
a finite set with more than one element
infinite
If z = x + iy, where x and y are real numbers and i = , then the points (x, y) for which is real, lie on
an ellipse
a circle
a parabola
a straight line
If a, band c are in AP, then the straight line ax + 2by + c = 0 will always pass through a fixed point whose coordinates are
(1, - 1)
(- 1, 1)
(1, - 2)
(- 2, 1)
The equation 2x2 + 5xy - 12y2 = 0 represents a
circle
pair of non-perpendicular intersecting straight lines
pair of perpendicular straight lines
hyperbola
If one end of a diameter of the circle 3x2 + 3y2 - 9x + 6y + y = 0 is (1, 2), then the other end is
(2, 1)
(2, 4)
(2, - 4)
(- 4, 2)
The line y = x intersects the hyperbola at the points P and Q. The eccentricity of ellipse with PQ as major axis and minor axis of length is
D.
Given equation of hyperbola and line are
respectively.
For intersection point of both curve put y = x, we get
Since, PQ is major axis, then its length
=
and length of minor axis is (given)
i.e., Major axis, 2a =
and minor axis, 2b =