A point moves, so that the sum of squares of its distance from the points (1, 2) and (- 2, 1) is always 6. Then, its locus is
the straight line
a circle with centre and radius
a parabola with focus (1, 2) and directrix passing through (- 2, 1)
an ellipse with foci (1, 2) and (- 2, 1)
A circle passing through (0, 0), (2, 6), (6, 2) cut the x-axis at the point P (0, 0). Then, the lenght of OP, where O is the origin, is
5
10
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 =
If the distance between the foci of an ellipse is equal to the length of the latusrectum, then its eccentricity is
The equation of the circle passing through the point (1, 1) and the points of intersection of x2 + y2 - 6x - 8 = 0 and x2 + y2 - 6 = 0 is
x2 + y2 + 3x - 5 = 0
x2 + y2 - 4x + 2 = 0
x2 + y2 + 6x - 4 = 0
x2 + y2 - 4y - 2 = 0
The area of the region bounded by the parabola y = x2 - 4x + 5 and the straight line y= x + l is
2
3
If the circles x2 + y2 + 2x + 2ky + 6 = 0 and x2 + y2 + 2ky + k = 0 intersect orthogonally, then k is equal to
If four distinct points (2k, 3k), (2, 0), (0, 3), (0, 0) lie on a circle, then
k < 0
0 < k < 1
k = 1
k > 1