Question

Equation of the line passing through the points $(2,3)$ and making intercept of $2$ units between the lines $y+2x=3,y+2x=5$ is

• A. $x=2$
• B. $y=3$
• C. $x+y=5$
• D. $x+y=7$

Answer 1

The correct option is A $x=2$

$\frac{S_n}{S_n^{\prime }}=\frac{5n+4}{9n+6}$

$\frac{\frac{n}{2}[2a+(n-1\left)d\right]}{\frac{n}{2}[2a^{\prime }+(n-1\left)\right]d^{\prime }}=\frac{5n+4}{9n+6}$

$\frac{a+\left(\frac{n-1}{2}\right)d}{a+\left(\frac{n-1}{2}\right)d^{\prime }}=\frac{5n+4}{9n+6}$........(i)

$\frac{a+17d}{a+17d^{\prime }}=\frac{5\left(35\right)+4}{9\left(35\right)+6}=\frac{179}{321}$

$\therefore \frac{T_{18}}{T_{18}^{\prime }}=\frac{179}{321}$

$\therefore \frac{T_{18}}{T_{18}^{\prime }}=\frac{a+17d}{a^{\prime }+17d^{\prime }}$...........(ii)

Comparing equation (i) and (ii),

$\frac{n-1}{2}=17$

$\therefore n-1=34$

$n=35$

$m=-2$

Let slope of line $PA=m$

$\tan \alpha =\frac{m_1-m_2}{1+m_1{m}_2}$

$\frac{1}{2}=\frac{m-(-2)}{1-2m}$

$2m+4=1-2m$

$4m=-3$

$m=-\frac{3}{4}$

Slope of line $PA=-\frac{3}{4}$

Equation of line which passes through $(2,3)$ and has slope $=-\frac{3}{4}$

$y-y_1=m(x-x_1)$

$y-3=-\frac{3}{4}(x-2)$

$4y-12=-3x+6$