The area (in square unit) of the triangle formed by x + y + 1 = 0 and the pair of straight lines x2 - 3xy + 2y2 = 0 is
The pairs of straight lines x2 - 3xy + 2y2 = 0 and x2 - 3xy + 2y2 + x - 2 = 0 form a
square but not rhombus
rhombus
parallelogram
rectangle but not a square
The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y -axes respectively are
x2 + y2 ± 4x ± 8y = 0
x2 + y2 ± 2x ± 4y = 0
x2 + y2 ± 8x ± 16y = 0
x2 + y2 ± x ± y = 0
The point (3 -4) lies on both the circles x2 + y2 - 2x + 8y + 13 = 0 and x2 + y2 - 4x + 6y + 11 = 0. Then, the angle between the circles is
135
The equation of the circle which passes through the origin and cuts orthogonally each of the circles x2 + y2 - 6x + 8 = 0 and x2 + y2 - 2x - 2y = 7 is
3x2 + 3y2 - 8x - 13y = 0
3x2 + 3y2 - 8x + 29y = 0
3x2 + 3y2 + 8x + 29y = 0
3x2 + 3y2 - 8x - 29y = 0
If the circle x2 + y2 = a intersects the hyperbola xy = c2 in four points (xi, yi), for i = 1, 2, 3 and 4, then y1 + y2 + y3 + y4 equals
0
c
a
c4
The mid point of the chord 4x - 3y = 5 of the hyperbola 2x2 - 3y2 = 12 is
(2, 1)
B.
(2, 1)
Given, 4x - 3y = 5 and 2x2 - 3y2 = 12