Straight Lines

The coordinates of the point on the curve y = x² - 3x + 2 where the tangent is perpendicular to the straight line y = x are 

• (0, 2)

• (1, 0)

• (- 1, 6)

• (2, - 2)

The equations of the lines through (1, 1) and making angles of 45° with the line x + y = 0 are

• x - 1 = 0, x - y = 0

• x - y = 0, y - 1 = 0

• x + y - 2 = 0, y - 1 = 0

• x - 1 = 0, y - 1 = 0

The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is

• 0

• 1

• 2

• $\infty$

The point (- 4, 5) is the vertex of a square and one of its diagonals is 7x - y + 8 = 0. The equation of the other diagonal is

• 7x - y + 23 = 0

• 7y + x = 30

• 7y + x = 31

• x - 7y = 30

A line through the point A(2, 0) which makes an angle of 30° with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15°. Then, the equation of the straight line in the new position is

• $\left(2 - \sqrt{3}\right)\mathrm{x} + \mathrm{y} - 4 + 2\sqrt{3} = 0$

• $\left(2 - \sqrt{3}\right)\mathrm{x} - \mathrm{y} - 4 + 2\sqrt{3} = 0$

• $\left(2 - \sqrt{3}\right)\mathrm{x} - \mathrm{y} + 4 + 2\sqrt{3} = 0$

• $\left(2 - \sqrt{3}\right)\mathrm{x} + \mathrm{y} + 4 + 2\sqrt{3} = 0$

The coordinates of the foot of the perpendicular from (0, 0) upon the line x + y = 2 are

• (2, - 1)

• (- 2, 1)

• (1, 1)

• (1, 2)

The line which is parallel to x - axis and crosses the curve y = $\sqrt{\mathrm{x}}$ at an angle 45°, is

• y = $\frac{1}{4}$

• $\mathrm{y} = \frac{1}{2}$

• y = 1

• y = 4

The distance between the lines 5x - 12y + 65 = 0 and 5x - 12y - 39 = 0 is

• 4

• 16

• 2

• 8

A particle is projected vertically upwards and is at a height h after t₁ seconds and again after t₂ seconds, then

• h = gt₁t₂

• h = $\frac{1}{2}{\mathrm{gt}}_1{\mathrm{t}}_2$

• $\mathrm{h} = \frac{2}{\mathrm{g}}{\mathrm{t}}_1{\mathrm{t}}_2$

• h = $\sqrt{{\mathrm{gt}}_1{\mathrm{t}}_2}$

The equation of bisectors of the angles between the lines $\left|\mathrm{x}\right| = \left|\mathrm{y}\right|$ are

• $\mathrm{y} = \pm \mathrm{x} \mathrm{and} \mathrm{x} = 0$

• $\mathrm{x} = \frac{1}{2} \mathrm{and} \mathrm{y} = \frac{1}{2}$

• y = 0 and x = 0

• None of the above