**RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1**: “A straight line is a curve such that every point on the line segment joining any two points lies on it is termed as a straight line”. In this chapter, we will discuss concepts related to straight lines, with examples for better understanding. RD Sharma Class 11 Maths Solutions contains all the solutions to the math problems given in the textbook. The subject matter experts have accurately prepared and solved the questions in each section. Students can consult and download RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 in PDF from the link given below and start offline practice.

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## Download RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 PDF:

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## Access RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1

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## RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1: Important Topics From The Chapter

**First Degree Equation**

Every first degree equation like ax+by+c=0ax+by+c=0 would be the equation of a straight line.

**Slope of a line**

- Slope (m) of a non-vertical line passing through the points (x1 ,y1 )(x1 , y1 ) and (x2 , y2)(x2 , y2) is given by is given by m =y1−y2x1−x2= m =y1−y2x1−x2= x1≠x2x1≠x2.
- If a line makes an angle á with the positive direction of x-axis, then the slope of the line is given by m =tanα, α≠90om =tanα, α≠90o
- Slope of horizontal line is zero and slope of vertical line is undefined.
- An acute angle (say θ) between lines L1 and L2L1 and L2with slopes m1 and m2m1 and m2 is given by tanθ=∣∣m2−m11+m1m2∣∣tanθ=|m2−m11+m1m2|, 1+m1m2≠01+m1m2≠0
- Two lines are parallel if and only if their slopes are equal i.e., m1=m2m1=m2
- Two lines are perpendicularif and only if product of their slopes is –1, i.e., mm2=−1m1.m2=−1
- Three points A, B and C are collinear, if and only if slope of AB = slope of BC.
- Equation of the horizontal line having distance a from the x-axis is eithery = a or y = – a.
- Equation of the vertical line having distance b from the y-axis is eitherx = b or x = – b.
- The point (x, y) lies on the line with slope m and through the fixed point (xo,y0 ),(xo, y0 ), if and only if its coordinates satisfy the equation.

** Various forms of equations of a line**:

: Equation of the line passing through the points (x1,y1)(x1, y1) and ((x2, y2)(x2, y2) is given by y−y1=y2−y1x2−x1(x−x1)y−y1=y2−y1x2−x1(x−x1)**Two points form**: The point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y=mx +cy=mx +c.**Slope-Intercept form**- If a line with slope m makes x-intercept d. Then equation of the line is y=m(x -d)y=m(x -d).
: Equation of a line making intercepts a and b on the x-and y-axis, respectively, is xa+yb=1xa+yb=1.**Intercept form**: The equation of the line having normal distance from origin p and angle between normal and the positive x−axis ωx−axis ωis given by x cosω +ysin ω=p x cosω +ysin ω=p**Normal form**: Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is called the general linear equation or general equation of a line.**General Equation of a Line**:**Working Rule for reducing general form into the normal form**

(i) Shift constant ‘C’ to the R.H.S. and get Ax+By=−CAx+By=−C

(ii) If the R.H.S. is not positive, then make it positive by multiplying the whole equation by -1.

(iii) Divide both sides of equation by A2+B2−−−−−−−√A2+B2.

The equation so obtained is in the normal form.

: x−x1cosθ=y−y1sinθ=rx−x1cosθ=y−y1sinθ=r**Parametric Equation (Symmetric Form)**: y=mxy=mxor y=xtanθy=xtanθ.**Equation of a line through origin**- The perpendicular distance (d) of a line Ax + By+ C = 0 from a point (x1, y1) (x1, y1) is given by d=|Ax1+By1+C|A2+B2√d=|Ax1+By1+C|A2+B2
- Distance between the parallel lines Ax + By + C1Ax + By + C1= 0 and Ax + By + C2Ax + By + C2= 0, is given by d=|C1−C2|A2+B2√d=|C1−C2|A2+B2

**Concurrent Lines**

Three of more straight lines are said to be concurrent if they pass through a common point i.e., they meet at a point. Thus, if three lines are concurrent the point of intersection of two lines lies on the third line.

** Condition of concurrency of three lines**:

a1(b2c3−b3c2)+b1(c2a3−c3a2)+c1(a2b3−a3b2)=0a1(b2c3−b3c2)+b1(c2a3−c3a2)+c1(a2b3−a3b2)=0

**EQUATIONS OF FAMILY OF LINES THROUGH THE INTERSECTION OF TWO LINES**

A1x+B1y+C1+k(A2x+B2y+C2)=0A1x+B1y+C1+k(A2x+B2y+C2)=0

where kk is a constant and also called parameter.

This equation is of first degree of xx and yy, therefore, it represents a family of lines.

**DISTANCE BETWEEN TWO PARALLEL LINES**

Working Rule to find the distance between two parallel lines:

(i) Find the co-ordinates of any point on one of ht egiven line, preferably by putting x=0x=0 and y=0y=0.

(ii) The perpendicular distance of this point from the other line is the required distance between the lines.

We have included all the information regarding CBSE RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1. If you have any query feel free to ask in the comment section.

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