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

Equation of curve in polar coordinates is $\frac{\mathrm{l}}{\mathrm{r}} = 2{\sin }^2\left(\frac{\mathrm{\theta }}{2}\right)$ represents

• a straight line

• a parabola

• a circle

• an ellipse

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 equation of the circle of radius 5 and touching the co-ordinate axes in third quadrant is

• (x - 5)²+ (y + 5)² = 25 

• (x + 5)² + (y + 5)² = 25

• (x + 4)² + (y + 4)² = 25

• (x + 6)² + (y + 6)² = 25

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

• 3

• 1

• - 2

• 2

A line is at a constant distance c from the origin and meets the coordinate axes in A and B. The locus of the centre of the circle passing through O, A, B is

• x² + y² = c²

• x² + y² = 2c²

• x² + y² = 3c²

• x² + y² = 4c²

The line y = mx + c intercepts the circle x² + y² = r² in two distinct points, if

• $- \mathrm{r}\sqrt{1 + {\mathrm{m}}^2} < \mathrm{c} < \mathrm{r}\sqrt{1 + {\mathrm{m}}^2}$

• $\mathrm{c} < - \mathrm{r}\sqrt{1 + {\mathrm{m}}^2}$

• $\mathrm{c} < \mathrm{r}\sqrt{1 + {\mathrm{m}}^2}$

• None of the above

The equation of the parabola with the focus (3, 0) and the directrix x + 3 = 0, is

• ${\mathrm{y}}^2 = 3\mathrm{x}$

• ${\mathrm{y}}^2 = 6\mathrm{x}$

• ${\mathrm{y}}^2 = 12\mathrm{x}$

• ${\mathrm{y}}^2 = 2\mathrm{x}$

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