The eccentricity of ellipse $\frac{{\mathrm{x}}^2}{16} + \frac{{\mathrm{y}}^2}{9} = 1$ is

• $\frac{7}{16}$

• $\frac{5}{4}$

• $\frac{\sqrt{7}}{4}$

• $\frac{\sqrt{7}}{2}$

The products of lengths of perpendiculars from any point of hyperbola x² - y² = 8 to its asymptotes, is

• 2

• 3

• 4

• 8

The equation 16x² + y² + 8xy - 74x - 78y + 212 = 0 represents

• a circle

• a parabola

• an ellipse

• a hyperbola

iF a is a complex number and b is a real number, then the equation $\overline{\mathrm{a}} + \mathrm{a} + \mathrm{b} = 0$ represents a

• straight line

• parabola

• circle

• hyperbola

The four distinct points (0, 0), (2, 0), (0, - 2)and (k, - 2) are concyclic, if k is equal to

• 3

• 1

• - 2

• 2

If e and e' are the eccentricities of the ellipse 5x² + 9y² = 45 and the hyperbola 5 - 4y = 45 respectively, then ee' is equal to

• 1

• 4

• 5

• 9

267.

If 5x - 12y + 10 = 0 and 12y - 5x + 16 = 0 are two tangents to a circle, then the radius of the circle is

• 1

• 2

• 4

• 6

The eccentricity of the ellipse 9x² + 5y² - 18x - 20y - 16 = 0, is:

• $\frac{1}{2}$

• $\frac{2}{3}$

• $\frac{3}{2}$

• $2$

The equation of the parabola with focus (0, 0)and directrix x + y = 4 is

• ${\mathrm{x}}^2 + {\mathrm{y}}^2 - 2\mathrm{xy} + 8\mathrm{x} +8\mathrm{y} -16 = 0$

• ${\mathrm{x}}^2 + {\mathrm{y}}^2 - 2\mathrm{xy} + 8\mathrm{x} + 8\mathrm{y} = 0$

• ${\mathrm{x}}^2 + {\mathrm{y}}^2 + 8\mathrm{x} + 8\mathrm{y} - 16= 0$

• ${\mathrm{x}}^2 - {\mathrm{y}}^2 + 8\mathrm{x} +8\mathrm{y} - 16= 0$

If P₁, P₂, P₃ are the perimeters of the three circles 

x² + y² + 8x - 6y = 0, 4x² + 4y - 4x - 12y - 186 = 0 and x² + y - 6x + 6y - 9 = 0 respectively, then

• ${\mathrm{P}}_1 < {\mathrm{P}}_2 < {\mathrm{P}}_3$

• ${\mathrm{P}}_1 < {\mathrm{P}}_3 < {\mathrm{P}}_2$

• ${\mathrm{P}}_3 < {\mathrm{P}}_2 < {\mathrm{P}}_1$

• ${\mathrm{P}}_2 < {\mathrm{P}}_3 < {\mathrm{P}}_1$