The distance between the directrices of the ellipse $\frac{{\mathrm{x}}^2}{4} + \frac{{\mathrm{y}}^2}{9} = 1$ is

• $\frac{9}{\sqrt{5}}$

• $\frac{18}{\sqrt{5}}$

• $\frac{24}{\sqrt{5}}$

• None of these

The equation of the normal to the hyperbola x² - 16y² - 2x - 64y - 72 = 0 at the point (- 4, - 3) is

• 5x + 16y + 79 = 0

• 16x + 5y + 97 = 0

• 16x + 5y + 79 = 0

• 5x + 16y + 97 = 0

The centre of the circle which circumscribes the square formed by x² - 8x + 12 = 0 and y² - 14y + 45 = 0 is

• (4, 5)

• (3, 4)

• (9, 5)

• (4, 7)

If e₁ and e₂ are the eccentricities of the hyperbolas $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2} - \frac{{\mathrm{y}}^2}{{\mathrm{b}}^2} = 1 \mathrm{and} \frac{{\displaystyle {\mathrm{x}}^2}}{{\displaystyle {\mathrm{a}}^2}} - \frac{{\displaystyle {\mathrm{y}}^2}}{{\displaystyle {\mathrm{b}}^2}} = - 1$, then the value of $\frac{1}{{{\mathrm{e}}_1}^2} + \frac{1}{{{\mathrm{e}}_2}^2}$ is

• 3

• 2

• 1

• $\frac{1}{2}$

The point of contact of 3x + 4y + 7 = 0 and x² + y² - 4x - 6y -12 = 0 is

• (1, 1)

• (- 1, 1)

• (1, - 1)

• ( -1, - 1)

The equation x² - 7xy + 12y² = 0 represents a

• circle

• pair of parallel straight lines

• pair of perpendicular straight lines

• pair of non-perpendicular straight lines

The locus of z given by $\left|\frac{\mathrm{z} - 1}{\mathrm{z} +\hspace{0.17em}1}\right|$ = 1 is

• a parabola

• an ellipse

• a circle

• a straight line

A conic section represents a circle, if its eccentricity e is

• e < 0

• e > 0

• e = 0

• None of these

The equation of circle passing through the points (0, 2) (3, 3) and having its centre on the x-axis is

• x² + y² - 14x - 12 = 0

• 3x² + 3y² - 22x - 4 = 0

• 3x² + 3y² - 14x - 12 = 0

• None of the above

The equation of a circle passing through origin and radius is a, is

• (x - a)² + (y - a)² = a²

• x² + y² = a²

• (x - a)² + y² = a²

• None of the above