General Form of a Straight Line

Q.

Equation of the hour hand at $4$ O’ clock is

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

Q.

The point (4, 5) lies on the graph of the equation 5y = ax + 9. Find the value of a.

1. 3

2. 4

3. -4

4. 5

Q. For the equation of straight line $2x-3y+5=0$, match the following.

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

Q. If a line passes through the point $(3,-5)$ and is parallel to $x-$axis, find its equation.

Q. If a, b, and c are in AP, then the straight line $ax+by+c=0$ will always pass through a fixed point whose coordinates are___

1. (1, 2)
2. (1, -2)
3. (-1, 2)
4. (2, 1)

Q. If the coordinates of the points A and B be (3, 3) and (7, 6), then the length of the portion of the line AB intercepted between the axes is

1. $\frac{5}{4}$
2. None of these
3. $\frac{\sqrt{10}}{4}$
4. $\frac{\sqrt{13}}{3}$

Q. Consider a $△ABC$ in the $xy$-plane with vertices $A=(0,0),B=(1,1)$ and $C=(9,1)$. If the line $x=a$ divides the triangle into two parts of equal area, then $a$ equals:

1. $3$
2. $3.5$
3. $4$
4. $4.5$

Q.

For $a>b>c>0$, the distance between (1, 1) and the point of intersection of the lines $ax+by+c=0$ and $bx+ay+c=0$ is less than $2\sqrt{2}$. Then,

1. $a+b-c>0$

2. $a-b+c<0$

3. $a-b+c>0$

4. $a+b-c<0$

Q. If a line passes through the point $(2,-3)$ and is parallel to $x-$axis, find its equation.

Q. Let $a,b,c$ be real numbers with $a^2+b^2+c^2=1$ Show that the equation $\left|\begin{array}{ccc}ax-by-c& bx+ay& cx+a\\ bx+ay& -ax+by-c& cy+b\\ cx+a& cy+b& -ax-by+c\end{array}\right|$ = 0
represents a straight line.

Q. A parallelogram is formed by the lines $a{x}^2+2hxy+b{y}^2=0$ and the lines through $(p,q)$ parallel to them and the equation of the diagonal of the parallelogram which doesn't pass through origin is $(\lambda x-p)(ap+hq)+(\mu y-q)(hp+bq)=0$, then find the value of ${\lambda }^3+{\mu }^3$.

Q. The straight lines x + y = 0, 3x + y-4 = 0, and x + 3y - 4 = 0 form a triangle which is

1. isosceles
2. equilateral
3. Right-angled
4. None of these

Q. The y-intercept of the straight line 2x + 8y = 32 is .

1. 4
2. 8
3. 16
4. 32

Q. If a line passes through the point $(1,-2)$ and is parallel to $x-$axis, find its equation.

Q. If a line passes through the point $(a,b)$ and is parallel to $x-$axis, find its equation.