The length of latusrectum of parabola y² + 8x - 2y + 17 = 0 is

• 2

• 4

• 8

• 16

If the normal to the parabola y² = 4x at P(1, 2) meets the parabola again in Q, then coordinates of Q are

• (- 6, 9)

• (9, - 6)

• (- 9, - 6)

• (- 6, - 9)

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

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

467.

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