Straight Lines

The equation of the pair of straight lines parallel to x-axis and touching the circle x² + y²- 6x - 4y -12 = 0 is

• y² - 4y - 21 = 0

• y² + 4y - 21 = 0

• y² - 4y + 21 = 0

• y² + 4y + 21 = 0

If the foot of the perpendicular from the origin to a straight line is at the point (3 - 4). Then, the equation of the line is

• 3x - 4y = 25

• 3x - 4y + 25 = 0

• 4x + 3y - 25 = 0

• 4x - 3y + 25 = 0

The angle between lines joining origin and intersection points of line 2x + y = 1 and curve 3x² + 4yx - 4x + 1= 0 is

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

The equation of the bisector of the acute angle between the lines 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 is

• 99x - 27y - 81 = 0

• 11x - 3y + 9 = 0

• 21x + 77y - 101 = 0

• 21x + 77y + 101 = 0

The angle between the straight lines

$\mathrm{x} - \mathrm{y}\sqrt{3} = 5 \mathrm{and} \sqrt{3}\mathrm{x} + \mathrm{y} = 7$ is

• 90$°$

• $60°$

• $75°$

• $30°$

The value of k so that x² + y² + kx + 4y + 2 = 0 and 2(x² + y) - 4x - 3y + k = 0 cut orthogonally is

• $\frac{10}{3}$

• $\frac{- 8}{3}$

• $\frac{- 10}{3}$

• $\frac{8}{3}$

If the lines $\frac{\mathrm{x} - 1}{2} = \frac{\mathrm{y} + 2}{3} = \frac{\mathrm{z} - 1}{4}$ and $\frac{\mathrm{x} - 3}{1} = \frac{\mathrm{y} - \mathrm{k}}{2} = \frac{\mathrm{z}}{1}$ intersect, then the value of k is

• 3/2

• 7/2

• - 2/7

• - 3/2

If $\mathrm{\alpha } + \mathrm{\beta } + \mathrm{\gamma } = \mathrm{a\delta } \mathrm{and} \mathrm{\beta } + \mathrm{\gamma } + \mathrm{\delta } = \mathrm{b\alpha }, \mathrm{\alpha } \mathrm{and} \mathrm{\delta }$ are non-collinear, then $\mathrm{\alpha } + \mathrm{\beta } + \mathrm{\gamma } + \mathrm{\delta }$ equals

• 0

• $\mathrm{a\alpha }$

• b$\mathrm{\delta }$

• (a + b)$\mathrm{\gamma }$

The two lines x = my + n, z = py + q and x = m'y + n', z =p'y + q' are perpendicular to each other, if

• mm' + pp' = 1

• $\frac{\mathrm{m}}{\mathrm{m}\text{'}} + \frac{\mathrm{p}}{\mathrm{p}\text{'}} = - 1$

• $\frac{\mathrm{m}}{\mathrm{m}\text{'}} + \frac{\mathrm{p}}{\mathrm{p}\text{'}} = 1$

• mm' + pp' = - 1

The shortest distance between the lines $\frac{\mathrm{x} - 7}{3} = \frac{\mathrm{y} + 4}{- 16} = \frac{\mathrm{z} - 6}{7}$ and $\frac{\mathrm{x} - 10}{3} = \frac{\mathrm{y} - 30}{8} = \frac{4 - \mathrm{z}}{5}$ is

• $\frac{234}{7}$ units

• $\frac{288}{21}$ units

• $\frac{221}{3}$ units

• $\frac{234}{21}$ units