If the slope of one lne is twice the slope of other in the pair of straight lines ax² + 2hxy + by² = 0, then 8h² is equal to

• - 9ab

• 9ab

• - 7ab

• 7ab

If the extremities of diagonal of a square (1, - 2, 3), (2, - 3, 5), then the length of its side, is

• $\sqrt{6}$

• $\sqrt{3}$

• $\sqrt{5}$

• $\sqrt{7}$

The foot of the perpendicular from (0, 2, 3) to the line $\frac{\mathrm{x} + 3}{5} = \frac{\mathrm{y} - 1}{2} = \frac{\mathrm{z} +\hspace{0.17em}4}{3}$ is

• (- 2, 3, 4)

• (2, - 1, 3)

• (2, 3, - 1)

• (3, 2, - 1)

If a line makes angle $\frac{\mathrm{\pi }}{3} \mathrm{and} \frac{\mathrm{\pi }}{4}$ with the X-axis and Y-axis respectively, then the angle made by the line with the Z-axis is

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{5\mathrm{\pi }}{12}$

• $\frac{\mathrm{\pi }}{3}$

The equation of the normal to the circle x² + y² + 6x + 4y - 3 = 0 at (1, - 2) is

• y + 1 = 0

• y + 2 = 0

• y + 3 = 0

• y - 2 = 0

The limiting points of the co-axial system containing the two circles x² + y² + 2x - 2y + 2 = 0 and 25(x² + y) - 10x - 80y + 65 = 0 are

• (1, - 1), (- 3, - 40)

• $\left(1, - 1\right), \left(- \frac{1}{5}, \frac{8}{5}\right)$

• $\left(- 1, 1\right), \left(\frac{1}{5}, \frac{8}{5}\right)$

• $\left(- \frac{1}{5}, - \frac{8}{5}\right)$

The radical axis of circles x² + y² + 5x + 4y - 5 = 0 and x² + y² - 3x + 5y - 6 = 0 is

• 8y - x + 1 = 0

• 8x - y+ 1 = 0

• 8x - 8y + 1 = 0

• y - 8x + 1 = 0

18.

If the polar of a point on the circle x² + y² = p² with respect to the circle x² + y² = q² touches the circle x² + y² = r, then p, q, r are in

• AP

• GP

• HP

• AGP

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)