The lines y = 2x + and 2y + x = 8 touch the ellipse x2 + y2 = 1. If the point of intersection of these two lines lie on a circle, whose centre coincides with the centre of that ellipse, then the equation of that circle is
The equation of the pair of lines through the point (2, 1) and perpendicular to the pair of lines 4xy + 2x + 6y + 3 = 0 is
xy - x - 2y + 2 = 0
xy + x - 2y - 2 = 0
xy + x + 2y - 6 = 0
xy - x + 2y - 2 = 0
The harmonic mean of two numbers is and their geometric mean is 2. The quadratic equation whose roots are twice those numbers is
C.
For the function f(x) = (x - 1)(x - 2) defined on [0, ½] the value of c satisfying Lagrange's mean value theorem is
If the roots of the equation x2 -7x2 + 14x - 8 = 0 are in geometric progression, then the difference between the largest and the smallest roots is
4
2
3