# Slope of a Line

## Trending Questions

**Q.**Find the slope of the line, which makes an angle of 30° with the positive direction of y -axis measured anticlockwise.

**Q.**

If the line (x-y+1) + k (y-2x+4) = 0 makes equal intercept on the axes then the value of k is

1/3

3/4

1/2

2/3

**Q.**

If 4a+5b+6c=0 then the set of lines ax+by+c=0 are concurrent at the point

**Q.**

Find equation of the line parallel to the line 3x - 4y + 2 = 0 and passing through the point (-2, 3).

**Q.**

Find the equation of a line whose perpendicular distance from the origin is √8 units and the angle between the positive direction of the x-axis and the perpendicular is 135∘.

**Q.**

Using slopes, show that the vertices (-2, -1), (4, 0), (3, 3) and (-3, 2) are the vertices of a parallelogram.

**Q.**

Find the perpendicular distance from the origin of the line joining the points (cos θ, sin θ) and (cos ϕ, sin ϕ).

**Q.**Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).

**Q.**

Find the equation of line passing through (2, 3) and perpendicular to the line 3x + 4 y - 5 = 0.

**Q.**If w_1 and w_2 are complex slopes of any two line in argand plane such that they make π/4 angle with each other then show that w_1=\pm i w_2

**Q.**A square with each side equal to a lies above the x-axis and has one vertex at the origin. One of the sides passing through the origin makes an angle α(0<α<π4) with the positive direction of the x-axis. Equation of a diagonal of the square is

y(cos α−sin α)=x(sin α+cos α)

y(sin α+cos α)+x(cos α−sin α)=a

x(cos α−sin α)=y(cos α+sin α)

x(cos α−sin α)−y(cos α+sin α)=a

**Q.**

Find the value of expression

sin(−θ)+cos(−θ)+sec(−θ)

+sin(π−θ)+cos(π−θ)+sec(π−θ)

0

2sinθ

2cosθ

2secθ

**Q.**In a plane, there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B, besides no three lines pass through one point, no line passes through both points A and B no two lines are parallel. Find the number of points of intersection of the straight lines.

**Q.**

The line xcosα+ysinα=p touches the hyperbola

x2a2−y2b2=1 if

a2cos2α−b2sin2α=p2

- a2cos2α−b2cos2α=2p
- a2cos2α−b2sin2α=p
- a2cos2α+b2sin2α=p

**Q.**

Find the equation of the lines through the point (3, 2) which make an angle of 45∘ with the line x - 2y = 3

**Q.**If the point (5, 2) bisects the intercept of a line between the axes, then its equation is

(a) 5x + 2y = 20

(b) 2x + 5y = 20

(c) 5x − 2y = 20

(d) 2x − 5y = 20

**Q.**

Which of the following statement is / are correct for equation 2x - 3y + 5 = 0

1. Slope of the straight line is 23

2. x-intercept of the straight line is −52

3. y-intercept of the straight line is 53

only 1 & 2

only 2 & 3

only 3 & 1

All 1, 2 & 3

**Q.**

identify the function based on the description.

1. It is periodic with period 2π

2. Domain of the function is R−nπ where nϵz

3. Range of the function is R-(-1, 1)

4. The graphs of F(x) tends to meet y-axis at ∞ at x=0, ±π, ±2π, .....

5. If x2>x1 then F(x2)>F(x1) when xϵ[π2, π)

6. if x2>x1 then F(x1)>F(x2) when xϵ(0, π2]

**Q.**If the centroid of an equilateral triangle is (1, 1) and its one vertex is (−1, 2), then the equation of its circumcircle is

(a) x

^{2}+ y

^{2}− 2x − 2y − 3 = 0

(b) x

^{2}+ y

^{2}+ 2x − 2y − 3 = 0

(c) x

^{2}+ y

^{2}+ 2x + 2y − 3 = 0

(d) none of these

**Q.**

Identify the function based on the description.

1. It is periodic with period 2π

2. Domain of the function is R−[nπ] where n ϵ z

3. Range of the function is R-(-1, 1)

4.The graphs of F(x) tends to meet y-axis at ∞ at x=0, ±π, ±2π, ......

5. If x2>x1 then F(x2)>F(x1) when x ϵ [π2, π)

6.If x2>x1 then F(x1)>F(x2) when x ϵ (0, π2]

**Q.**Using the method of slope, show that the following points are collinear

(i) A (4, 8), B (5, 12), C (9, 28)

(ii) A (16, − 18), B (3, −6), C (−10, 6)

**Q.**If the straight line 3x+4y+5−k(x+y+3)=0 is parallel to y− axis, then the value of k is

**Q.**The circle x

^{2}+ y

^{2}− 2x − 2y + 1 = 0 is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in new-position.

**Q.**

A square with each side equal to a lies above the x-axis and has one vertex at the origin. One of the sides passing through the origin makes an angle α(0<α<π4) with the positive direction of the x-axis. Equation of a diagonal of the square is

y(cos α−sin α)=x(sin α+cos α)

y(sin α+cos α)+x(cos α−sin α)=a

x(cos α−sin α)=y(cos α+sin α)

x(cos α−sin α)−y(cos α+sin α)=a

**Q.**Find the slope of the line, which makes an angle of 30o with the positive direction of y-axis measured anticlockwise.

**Q.**The slope of the line formed by joining the points A(1, 3) and B(4, 7) is

- 43
- −43
- 34
- −34

**Q.**

If the line

(3x+14y+7)+k(5x+7y+6)=0

is parallel to the y-axis, then the value of k is

- 13
- −35
- −2
- 2

**Q.**Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.

**Q.**Find the equation of the lines through the point (3, 2) which make an angle of 45∘ with the line x−2y=3.

**Q.**Find the slope of a line perpendicular to the line whose slope is -5/6?