The axis of the parabola x² + 2xy + y² - 5x + 5y - 5 = 0 is

• x + y = 0

• x + y - 1 = 0

• x - y + 1 = 0

• $\mathrm{x} - \mathrm{y} = \frac{1}{\sqrt{2}}$

The line segment joining the foci of the hyperbola x^{2 -} y² + 1 = 0 is one of the diameters of a circle. The equation of the circle is

• x² + y² = 4

• x² + y² = $\sqrt{2}$

• x² + y² = 2

• x² + y² = $2\sqrt{2}$

If one of the diameters of the curve x² + y² - 4x - 6y + 9 = 0 is a chord of a circle with centre (1, 1), the radius of this circle is

• 3

• 2

• $\sqrt{2}$

• 1

Let A(- 1, 0) and B(2, 0) be two points. A point M moves in the plane in such a way that $\angle \mathrm{MBA} = 2\angle \mathrm{MAB}$. Then, the point M moves along

• a straight line

• a parabola

• an ellipse

• a hyperbola

The area of the figure bounded by the parabolas x = - 2y ² and x = 1- 3y² is

• $\frac{4}{3}$ sq. units

• $\frac{2}{3}$ sq. units

• $\frac{3}{7}$ sq. units

• $\frac{6}{7}$sq. units

Tangents are drawn to the ellipse $\frac{{\mathrm{x}}^2}{9} + \frac{{\mathrm{y}}^2}{5} = 1$ at the ends of both latusrectum. The area of the quadrilateral, so formed is

• 27 sq. units

• $\frac{13}{2}$ sq. units

• $\frac{15}{4}$ sq. units

• 45 sq. units

If the tangent to y² = 4ax at the point (at², 2at) where $\left|\mathrm{t}\right|$ > 1 is a normal to x² - y² = a² at the point ($\mathrm{a} \sec \left(\mathrm{\theta }\right), \mathrm{a} \tan \left(\mathrm{\theta }\right)$), then

• $\mathrm{t} = - \csc \left(\mathrm{\theta }\right)$

• $\mathrm{t} = - \sec \left(\mathrm{\theta }\right)$

• $\mathrm{t} = 2\tan \left(\mathrm{\theta }\right)$

• $\mathrm{t} = 2\cot \left(\mathrm{\theta }\right)$

The focus of the conic x- 6x + 4y + 1 = 0 is

• (2, 3)

• (3, 2)

• (3, 1)

• (1, 4)

249.

The line y = x + $\mathrm{\lambda }$ is tangent to the ellipse 2x² + 3y² = 1. Then, $\mathrm{\lambda }$ is

• - 2

• 1

• $\sqrt{\frac{5}{6}}$

• $\sqrt{\frac{2}{3}}$

The equation of a line parallel to the line 3x + 4y= 0 and touching the circle x² + y² = 9 in the first quadrant, is

• 3x +4y = 15

• 3x +4y = 45

• 3x +4y = 9

• 3x +4y = 27