The inclination of the straight line passing through the point (- 3, 6) and the mid point of the line joining the points ( 4, - 5) and (- 2, 9) is:

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{3\mathrm{\pi }}{4}$

A point moves such that the area of the triangle formed by it with the points (1, 5) and (3, - 7) is 21 sq unit Then locus of the point is :

• 6x + y - 32 = 0

• 6x - y + 32 = 0

• x + 6y - 32 = 0

• 6x - y - 32 = 0

183.

The line $\frac{\mathrm{x}}{\mathrm{a}} - \frac{\mathrm{y}}{\mathrm{b}}$ = 1 cuts the x-axis at P. The equation of the line through P perpendicular to the given line is :

• x + y = ab

• x + y = a + b

• ax + by = a²

• bx + ay = b²

The value of $\mathrm{\lambda }$. for which the lines 3x + 4y = 5, 2x + 3y = 4and $\mathrm{\lambda }$x + 4y = 6 meet at a point, is :

• 2

• 1

• 4

• 3

Three vertices of a parallelogram taken in order are (- 1, -  6), (2, - 5) and (7, 2). The fourth vertex is :

• (1, 4)

• (1, 1)

• (4, 4)

• (4, 1)

The orthocentre of the triangle whose vertices are (5, - 2), - 1, 2) and (1, 4), is :

• $\left(- \frac{1}{5}, \frac{16}{5}\right)$

• $\left(\frac{14}{5}, \frac{1}{5}\right)$

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

• $\left(\frac{14}{5}, \frac{14}{5}\right)$

Distance between the lines 5x + 3y - 7 = 0 and 15x + 9y + 14 = 0 is :

• $\frac{35}{\sqrt{34}}$

• $\frac{1}{3\sqrt{34}}$

• $\frac{35}{3\sqrt{34}}$

• $\frac{35}{2\sqrt{34}}$

If the equation 2x² + 7 xy + 3y² - 9 x - 7y + k = 0 represents a pair of lines, then k is equal to

• 4

• 2

• 1

• - 4

The angle between the lines 2x - y + 3 = 0 and x + 2y + 3 = 0 is :

• 90°

• 60°

• 45°

• 30°

Distance between the pair of lines represented by the equation x² - 6xy + 9y² + 3 - 9y - 4 = 0 is:

• $\frac{15}{\sqrt{10}}$

• $\frac{1}{2}$

• $\sqrt{\frac{5}{2}}$

• $\frac{1}{\sqrt{10}}$