KC Sinha Mathematics Solution Class 11 Chapter 21 Straight Lines Exercise 21.5

 Exercise 21.5

Page no 21.56

Question 1

Reduce each of the following equations into slope-intercept form :

(i) $7 x+3 y-6=0$

(ii) $6 x+3 y-5=0$

(iii) $3 x+3 y=5$

(iv) $2 x-4 y=5$

(v) $y=0$

(vi) $x+7 y=0$

Question 2

Reduce the following equations to the intercept form :

(i) $2 x-3 y=5$

(ii) $3 x-4 y=10$

(iii) $\sqrt{3} y-3 x=3$

(iv) $4 x-3 y=6$

(v) $3 y+2=0$

(vi) $3 x+2 y-12=0$

Question 3

Reduce each of the following equations to the normal form and find the length of the perpendicular from origin to the line :

(i) $\sqrt{3} x+y-8=0$

(ii) $4 x+3 y-9=0$

(iii) $3 x-4 y+10=0$

(iv) $x+y-2=0$

(v) $y-2=0$

(vi) $x-4=0$

(vii) $x-y=4$

(viii) $x-\sqrt{3} y+8=0$

(ix) $\sqrt{3} x+y+2=0$

Page no 21.57

Question 4

Equation of a line is $3 x-4 y+10=0$. Find its

(i) slope

(ii) $x$ and $y$-intercepts

Question 5

For the straight line $8 x-15 y+51=0$, find the length of the perpendicular from the origin to this line and the tangent of the inclination of this perpendicular with the $x$-axis.

Question 6

Find the equation of the line joining the points $(1,2)$ and $(-3,1)$. Find its intercepts on the axes. If $p$ be the length of the perpendicular from the origin wo the line find the value of $p$.