# Point Slope Form of a Line

## Trending Questions

**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

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

$\sqrt{17}$

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

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

**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

**Q.**

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

$x-y=5$

$x+y=5$

$x+y=1$

$x-y=1$

**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

- x−√3y+2√3−1=0
- √3x+y−√3−2=0
- √3x−y+2−√3=0
- x+√3y−2√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 :

- (x2+y2)3=4R2x2y2
- (x2+y2)2=4R2x2y2
- (x2+y2)2=4Rx2y2
- (x2+y2)(x+y)=R2xy

**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

$x-y-2=0$

$x-y+12=0$

$x+y-12=0$

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 $(\mathrm{cos}\theta ,\mathrm{sin}\theta )$ and $(\mathrm{cos}\varphi ,\mathrm{sin}\varphi )$.

**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 :

- 4√5
- √54
- 2√5
- √52

**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

$1:2$

$2:1$

$4:2$

$4:3$

**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

- √3x+y=4
- x+√3y+4=0
- x+√3y=4
- x−√3y=4

**Q.**

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

$1$

$2$

$3$

$\frac{1}{2}$

**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

$5x+3y+15=0$

$3x+5y+15=0$

$5x+3y\u201315=0$

$3x+5y\u201315=0$

**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

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

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

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

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

**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∘ 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

$1$

$-1$

$0$

**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 :

- (x2+y2)3=4R2x2y2
- (x2+y2)2=4R2x2y2
- (x2+y2)2=4Rx2y2
- (x2+y2)(x+y)=R2xy

**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 13 and x− intercept is 4 will be

- x−3y+12=0
- x−6y−2=0
- 4x−y−16=0
- x−3y−4=0

**Q.**The equation of the straight line, which passes through the point (2, 4) and makes an angle θ with positive xaxis where cosθ=−13 is

- 2√2x−y−2√2+4=0
- 2√2x+y−4√2−4=0
- √2x+y−2√2−4=0
- x+2√2y−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)

- 18
- 16
- 10
- 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.