The equation of the tangent to the conic x² - y² - 8x + 2y + 11 = 0 at (2, 1) is

• x + 2 = 0

• 2x + 1 = 0

• x + y + 1 = 0

• x - 2 = 0

The total number of tangents through the point ( 3, 5) that can be drawn to the ellipses 3x² + 5y² = 32 and 25x + 9y² = 450 is

• 0

• 2

• 3

• 4

The equation of chord of the circle x² + y² - 4x = 0, whose mid-point is (1, 0) is

• y = 2

• y = 1

• x = 2

• x = 1

The line y = 2t² intersects the ellipse $\frac{{\mathrm{x}}^2}{9} + \frac{{\mathrm{y}}^2}{4} = 1$ in real points, if

• $\left|\mathrm{t}\right| \le 1$

• $\left|\mathrm{t}\right| < 1$

• $\left|\mathrm{t}\right| > 1$

• $\left|\mathrm{t}\right| \ge 1$

The coordinates of the focus of the parabola described parametrically by x = 5t² + 2, y = 10t + 4 are

• (7, 4)

• (3, 4)

• (3, - 4)

• (- 7, 4)

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is 90°. The eccentricity of the ellipse is

• 1/8

• 1/√3

• √(2/3)

• √(1/2)

If the rate of increase of the radius of a circle is 5 cm/ s, then the rate of increase of its area, when the radius is 20 cm, will be

• 10$\mathrm{\pi }$

• 20$\mathrm{\pi }$

• 200$\mathrm{\pi }$

• 400$\mathrm{\pi }$

128.

The equation of the circle which passes through the points of intersection of the circles x² + y² - 6x = 0 and x² + y² - 6y = 0 and has its centre at $\left(\frac{3}{2}, \frac{{\displaystyle 3}}{{\displaystyle 2}}\right)$, is

• x² + y² + 3x + 3y + 9 = 0

• x² + y² + 3x + 3y = 0

• x² + y² - 3x - 3y = 0

• x² + y² - 3x - 3y + 9 = 0

If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the ellipse is

• $\sqrt{\frac{2}{3}}$

• $\sqrt{\frac{2}{5}}$

• $\sqrt{\frac{1}{3}}$

• $\sqrt{\frac{1}{2}}$

If t is a parameter, then x = $\mathrm{a}\left(\mathrm{t} + \frac{1}{\mathrm{t}}\right)$, y = $\mathrm{b}\left(\mathrm{t} - \frac{1}{\mathrm{t}}\right)$ represents

• an ellipse

• a circle

• a pair of straight lines

• a hyperbola