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 $\mathrm{y} - \frac{3}{2} = - 3\left(\mathrm{x} + \frac{1}{2}\right)$

• a circle with centre $\left(- \frac{1}{2}, \frac{3}{2}\right)$ and radius $\frac{1}{\sqrt{2}}$

• 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 $\ne$ (0, 0). Then, the lenght of OP, where O is the origin, is

• $\frac{5}{2}$

• $\frac{5}{\sqrt{2}}$

• 5

• 10

83.

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 $\frac{{\mathrm{x}}^2}{9} - \frac{{\mathrm{y}}^2}{25} = 1$ at the points P and Q. The eccentricity of ellipse with PQ as major axis and minor axis of length $\frac{5}{\sqrt{2}}$ is

• $\frac{\sqrt{5}}{3}$

• $\frac{5}{\sqrt{3}}$

• $\frac{5}{9}$

• $\frac{2\sqrt{2}}{9}$

If the distance between the foci of an ellipse is equal to the length of the latusrectum, then its eccentricity is

• $\frac{1}{4}\left(\sqrt{5} - 1\right)$

• $\frac{1}{2}\left(\sqrt{5} + 1\right)$

• $\frac{1}{2}\left(\sqrt{5} - 1\right)$

• $\frac{1}{4}\left(\sqrt{5} + 1\right)$

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

• $\frac{1}{2}$

• 2

• 3

• $\frac{9}{2}$

The equation y² + 4x + 4y + k = 0 represents a parabola whose latusrectum is

• 1

• 2

• 3

• 4

If the circles x² + y² + 2x + 2ky + 6 = 0 and x² + y² + 2ky + k = 0 intersect orthogonally, then k is equal to

• $2 \mathrm{or} - \frac{3}{2}$

• $- 2 \mathrm{or} - \frac{3}{2}$

• $2 \mathrm{or} \frac{3}{2}$

• $- 2 \mathrm{or} \frac{3}{2}$

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