Slope of a Line

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. 1/3

2. 3/4

3. 1/2

4. 2/3

Q.

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

1. 

2. 

3. 

4. 

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 $\sqrt{8}$ units and the angle between the positive direction of the x-axis and the perpendicular is ${135}^{\circ }$.

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 $(cos\theta ,sin\theta )$ and $(cos\varphi ,sin\varphi )$.

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 $\alpha (0<\alpha <\frac{\pi }{4})$ with the positive direction of the $x$-axis. Equation of a diagonal of the square is

1. $y(\cos \alpha -\sin \alpha )=x(\sin \alpha +\cos \alpha )$

2. $y(\sin \alpha +\cos \alpha )+x(\cos \alpha -\sin \alpha )=a$

3. $x(\cos \alpha -\sin \alpha )=y(\cos \alpha +\sin \alpha )$

4. $x(\cos \alpha -\sin \alpha )-y(\cos \alpha +\sin \alpha )=a$

Q.

Find the value of expression
$\sin (-\theta )+\cos (-\theta )+\sec (-\theta )$
$+\sin (\pi -\theta )+\cos (\pi -\theta )+\sec (\pi -\theta )$

1. 0

2. $2\sin \theta$

3. $2\cos \theta$

4. $2\sec \theta$

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 $x\cos \alpha +y\sin \alpha =p$ touches the hyperbola
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ if

1. $a^2{\cos }^2\alpha -b^2{\sin }^2\alpha =p^2$

2. $a^2{\cos }^2\alpha -b^2{\cos }^2\alpha =2p$
3. $a^2{\cos }^2\alpha -b^2{\sin }^2\alpha =p$
4. $a^2{\cos }^2\alpha +b^2{\sin }^2\alpha =p$

Q.

Find the equation of the lines through the point (3, 2) which make an angle of ${45}^{\circ }$ 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 $\frac{2}{3}$

2. x-intercept of the straight line is $\frac{-5}{2}$

3. y-intercept of the straight line is $\frac{5}{3}$

1. only 1 & 2

2. only 2 & 3

3. only 3 & 1

4. All 1, 2 & 3

Q.

identify the function based on the description.

1. It is periodic with period $2\pi$

2. Domain of the function is $R-n\pi$ where $nϵz$

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

4. The graphs of F(x) tends to meet y-axis at $\infty$ at x=0, $\pm \pi ,\pm 2\pi$, .....

5. If $x_2>x_1$ then $F\left(x_2\right)>F\left(x_1\right)$ when $xϵ[\frac{\pi }{2},\pi )$

6. if $x_2>x_1$ then $F\left(x_1\right)>F\left(x_2\right)$ when $xϵ(0,\frac{\pi }{2}]$

1. 

2. 

3. 

4. 

5. 

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) x² + y² − 2x − 2y − 3 = 0
(b) x² + y² + 2x − 2y − 3 = 0
(c) x² + y² + 2x + 2y − 3 = 0
(d) none of these

Q.

Identify the function based on the description.

1. It is periodic with period $2\pi$

2. Domain of the function is $R-\left[n\pi \right]$ where $nϵz$

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

4.The graphs of F(x) tends to meet y-axis at $\infty$ at $x=0,\pm \pi ,\pm 2\pi ,......$

5. If $x_2>x_1$ then $F\left(x_2\right)>F\left(x_1\right)$ when $xϵ[\frac{\pi }{2},\pi )$

6.If $x_2>x_1$ then $F\left(x_1\right)>F\left(x_2\right)$ when $xϵ(0,\frac{\pi }{2}]$

1. 

2. 

3. 

4. 

5. 

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 x² + y² − 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 $\alpha (0<\alpha <\frac{\pi }{4})$ with the positive direction of the $x$-axis. Equation of a diagonal of the square is

1. $y(\cos \alpha -\sin \alpha )=x(\sin \alpha +\cos \alpha )$

2. $y(\sin \alpha +\cos \alpha )+x(\cos \alpha -\sin \alpha )=a$

3. $x(\cos \alpha -\sin \alpha )=y(\cos \alpha +\sin \alpha )$

4. $x(\cos \alpha -\sin \alpha )-y(\cos \alpha +\sin \alpha )=a$

Q. Find the slope of the line, which makes an angle of ${30}^o$ 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 .

1. $\frac{4}{3}$
2. $\frac{-4}{3}$
3. $\frac{3}{4}$
4. $\frac{-3}{4}$

Q.

If the line
$(3x+14y+7)+k(5x+7y+6)=0$
is parallel to the y-axis, then the value of $k$ is

1. $\frac{1}{3}$
2. $\frac{-3}{5}$
3. $-2$
4. $2$

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 $45{}^{\circ }$ with the line $x-2y=3$.

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