Point Slope Form of a Line

Q.

The line$L$given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line $K$ is parallel to$L$and has the equation $\frac{x}{c}+\frac{y}{3}=1.$ Then, the distance between$L$and $K$ is

1. $\frac{23}{\sqrt{15}}$

2. $\sqrt{17}$

3. $\frac{17}{\surd 15}$

4. $\frac{23}{\surd 17}$

Q.

Find the equation of the line parallel to x-axis and passing through (3, -5).

Q.

Find the equation of the line passing through (0, 0) with slope m.

Q.

The combined equation of bisectors of angles between coordinate axes, is

1. 

2. 

3. 

4. 

Q.

The equation of the straight line passing through the point $(3,2)$ and perpendicular to the line $y=x$ is

1. $x-y=5$

2. $x+y=5$

3. $x+y=1$

4. $x-y=1$

Q. The equation of the line passing through
(1, 2) and making an angle of 30° in clockwise direction with the positive direction of y-axis is .

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

Q. If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B$, then the locus of the foot of perpendicular from $O$ on $AB$ is :

1. $(x^2+y^2{)}^3=4R^2{x}^2{y}^2$
2. $(x^2+y^2{)}^2=4R^2{x}^2{y}^2$
3. $(x^2+y^2{)}^2=4R{x}^2{y}^2$
4. $(x^2+y^2)(x+y)=R^{2}xy$

Q.

If the middle points of the sides $BC,CA$ and $AB$ of the triangle $ABC$ be $(1,3),(5,7)$ and $(-5,7)$respectively then the equation of the side $AB$ is

1. $x-y-2=0$

2. $x-y+12=0$

3. $x+y-12=0$

4. None of these.

Q.

Find the equation of the line perpendicular to x-axis and having intercept -2 on x-axis.

Q.

Find the perpendicular distance from the origin of the line joining the points $(\cos \theta ,\sin \theta )$ and $(\cos \varphi ,\sin \varphi )$.

Q. The straight line $x+2y=1$ meets the coordinate axes at $A$ and $B$. A circle is drawn through $A,B$ and the origin. Then the sum of perpendicular distances from $A$ and $B$ on the tangent to the circle at the origin is :

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

Q.

A line passing through origin and is perpendicular to two given lines $2x+y+6=0$ and $4x+2y-9=0$. The ratio in which the origin divides points of intersection of given lines and the line perpendicular to given lines, is

1. $1:2$

2. $2:1$

3. $4:2$

4. $4:3$

Q.

If the foot of perpendicular drawn from the point $(1,0,3)$ on a line passing through $(\alpha ,7,1)$ is $\left(\frac{5}{3},\frac{7}{3},\frac{17}{3}\right)$ then $\alpha$ is equal to:

Q. The coordinates of two consecutive vertices $A$ and $B$ of a regular hexagon $ABCDEF$ are $(1,0)$ and $(2,0),$ respectively. Then the equation of the diagonal $CE$ is

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

Q.

A straight line perpendicular to the line $2x+y=3$ is passing through $(1,1)$. Its $y-intercept$ is

1. $1$

2. $2$

3. $3$

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

Q.

Find the equations of the medians of a triangle, the coordinates of whose vertices are (-1, 6), (-3, -9) and (5, -8).

Q.

If $\left(\frac{3}{2},\frac{5}{2}\right)$ is the midpoint of the line segment intercepted by a line between axes, then the equation of the line is

1. $5x+3y+15=0$

2. $3x+5y+15=0$

3. $5x+3y–15=0$

4. $3x+5y–15=0$

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.

The pair of lines joining origin to the points of intersection of the two curves $a{x}^2+2hxy+b{y}^2+2gx=0$ and $a{x}^2+2hxy+b{y}^2+2gx=0$ will be at right angles, if

1. $\left(a+b\right)g=\left(a+b\right)g$

2. $\left(a+b\right)g=\left(a+b\right)g$

3. $h^2-ab=h{}^2-ab$

4. $a+b+h^2=a+b+h{}^2$

Q.

Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.

Q.

Find the equation of the straight line passing through $(3,-2)$ and making an angle of ${60}^{\circ }$ with the positive direction of $y$-axis.

Q.

Two lines are represented by equations $x+y=1$ and $x+ky=0$are mutually orthogonal if $k$ is

1. $1$

2. $-1$

3. $0$

4. None of these

Q. If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B$, then the locus of the foot of perpendicular from $O$ on $AB$ is :

1. $(x^2+y^2{)}^3=4R^2{x}^2{y}^2$
2. $(x^2+y^2{)}^2=4R^2{x}^2{y}^2$
3. $(x^2+y^2{)}^2=4R{x}^2{y}^2$
4. $(x^2+y^2)(x+y)=R^{2}xy$

Q.

Find the equation of the right bisector of the line segment joining the points A (1, 0) and B (2, 3).

Q. The equation of line whose slope is $\frac{1}{3}$ and $x-$ intercept is $4$ will be

1. $x-3y+12=0$
2. $x-6y-2=0$
3. $4x-y-16=0$
4. $x-3y-4=0$

Q. The equation of the straight line, which passes through the point $(2,4)$ and makes an angle $\theta$ with positive $x$axis where $\cos \theta =-\frac{1}{3}$ is

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

Q. A straight line $L$ with negative slope, passes through the point $(12,3)$ and cuts the positive coordinate axes at points $P$ and $Q$. As $L$ varies, the absolute minimum value of $OP+OQ$ is $(O$ is the origin$)$

1. $18$
2. $16$
3. $10$
4. $27$

Q.

The owner of a milk store finds that he can sell 980 liters milk each week at Rs 14 per liter and 1220 liters of milk each week at Rs 16 per liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17 per liter.

Q.

Find the equations to the altitudes of the triangle whose angular points are A (2, -2), B (1, 1) and C (-1, 0).

Q.

Find the equation of the straight line passing through the point (6, 2) and having slope -3.