Angle between Two Lines

Q.

A straight line L through the point (3, -2) is inclined at an angle ${60}^{\circ }$ to the line $\sqrt{3}x+y=1$. If L also intersects the X-axis, then the equation of L is

1. $y+\sqrt{3}x+2-3\sqrt{3}=0$

2. $y-\sqrt{3}x+2+3\sqrt{3}=0$

3. $\sqrt{3}y+x-3+2\sqrt{3}=0$

4. $\sqrt{3}y-x+3+2\sqrt{3}=0$

Q. The equations of two equal sides of an isosceles triangle are 7x – y + 3 = 0 and x + y –3 = 0 and the third side passes through the point (1, -10). The equation of the third side is

1. Neither 3x + y + 7 nor x – 3y – 31 = 0
2. 3x + y + 7 = 0 but not x – 3y – 31 = 0
3. x – 3y – 31 = 0 but not 3x + y + 7 = 0
4. 3x + y + 7 = 0 or x – 3y – 31 = 0

Q. A straight line L through the poit $(3,-2)$ is inclined at an angle ${60}^0$ to the line $\sqrt{3}x+y=1$. If L also intersects the x-axis, then the equation of L is

1. $y-\sqrt{3}x+2+3\sqrt{3}=0$
2. $\sqrt{3}y-x+3+2\sqrt{3}=0$
3. $\sqrt{3}y+x-3+2\sqrt{3}=0$
4. $y+\sqrt{3}x+2-3\sqrt{3}=0$

Q.

The equation of the pair of straight lines through origin, each of which makes as angle $\alpha$ with the line y = x, is

1. 

2. 

3. 

4. 

Q.

Let $PQR$ be a right angled isosceles triangle right angled at $P(2,1)$. If the equation of the line $QR$ is $2x+y=3$, then the equation representing the pair of lines $PQ$ and $PR$ is

1. $3x^2-3y^2+8xy+20x+10y+25=0$

2. $3x^2-3y^2+8xy-20x-10y+25=0$

3. $3x^2-3y^2+8xy+10x+15y+20=0$

4. $3x^2-3y^2-8xy-10x-15y-20=0$

Q.

The angle between the lines xy = 0 is

1. 

2. 

3. 

4. 

Q.

A straight line L through the point (3, -2) is inclined at an angle ${60}^{\circ }$ to the line $\sqrt{3}x+y=1$. If L also intersects the X-axis, then the equation of L is

1. $y+\sqrt{3}x+2-3\sqrt{3}=0$

2. $y-\sqrt{3}x+2+3\sqrt{3}=0$

3. $\sqrt{3}y-x+3+2\sqrt{3}=0$

4. $\sqrt{3}y+x-3+2\sqrt{3}=0$

Q.

The equation of the pair of straight lines through origin, each of which makes as angle $\alpha$ with the line y = x, is

1. 

2. 

3. 

4. 

Q.

The angle between the lines xy = 0 is

1. 

2. 

3. 

4. 

Q. The equations of two equal sides of an isosceles triangle are 7x – y + 3 = 0 and x + y –3 = 0 and the third side passes through the point (1, -10). The equation of the third side is

1. x – 3y – 31 = 0 but not 3x + y + 7 = 0
2. 3x + y + 7 = 0 but not x – 3y – 31 = 0
3. 3x + y + 7 = 0 or x – 3y – 31 = 0
4. Neither 3x + y + 7 nor x – 3y – 31 = 0