Straight Lines

Two lines $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4}$ and $\frac{\mathrm{x} - 3}{1} = \frac{\mathrm{y} - \mathrm{k}}{2} = \mathrm{z}$ intersect at a point, if k is equal to

• $\frac{2}{9}$

• $\frac{1}{2}$

• $\frac{9}{2}$

• $\frac{1}{6}$

The angle between lines joining the origin to the point of intersection of the line $\sqrt{3}$x + y = 2 and the curve y² - x² = 4 is

• ${\tan }^{-1}\left(\frac{2}{\sqrt{3}}\right)$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$6$}\right.$

• ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

The line 2x + $\sqrt{6}$y = 2 is a tanent to the curve x² - 2y² = 4. The point of contact is

• $\left(4, - \sqrt{6}\right)$

• $\left(7, - 2\sqrt{6}\right)$

• (2, 3)

• $\left(\sqrt{6}, 1\right)$

A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation is

• 3x - 4y + 7 = 0

• 4x + 3y = 24

• 3x + 4y = 25

• x + y = 7

The equation of straight line through the intersection of the lines x - 2y = 1 and x + 3y = 2 and parallel to 3x + 4y = 0 is

• 3x + 4y + 5 = 0

• 3x + 4y - 10 = 0

• 3x + 4y - 5 = 0

• 3x + 4y + 6 = 0

To the lines ax² + 2hxy + by² = 0, the lines a²x² + 2h(a + b) xy + b²y² = 0 are

• equally inclined

• perpendicular

• bisector of the angle

• None of these

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. What is its y intercept

• 1/3

• 2/3

• 1

• 4/3

The equation of straight line through the intersection of line 2x +y = 1 and 3x + 2y = 5 and passing through the origin is

• 7x + 3y = 0

• 7x - y = 0

• 3x + 2y = 0

• x + y = 0

The condition that the line lx + my = 1 may be normal to the curve y² = 4ax, is

• al³ - 2alm² = m²

• al² + 2alm³ = m²

• al³ + 2alm² = m³

• al³ + 2alm² = m²

If the lines $\frac{\mathrm{x} - 1}{2} = \frac{\mathrm{y} +\hspace{0.17em}1}{3} = \frac{\mathrm{z} - 1}{4}$ and $\frac{\mathrm{x} - 3}{2} = \frac{\mathrm{y} -\hspace{0.17em}\mathrm{k}}{3} = \frac{\mathrm{z}}{1}$ intersect, then the value of k, is

• $\frac{3}{2}$

• $\frac{9}{2}$

• $- \frac{2}{9}$

• - $\frac{3}{2}$