Question

The equation of the straight line passing through the intersection of straight lines x+2y=5 and 3x+7y=17 and perpendicular to line 3x+4y=10 is .

• A. 3x-4y+1=0
• B. 3x-4y-1=0
• C. 4x-3y+1=0
• D. 4x-3y+2=0

Answer 1

The correct option is D 4x-3y+2=0

The equation of the straight line passing through the intersection of straight lines x+2y=5 and 3x+7y=17 will be given by
$(x+2y-5)+\lambda (3x+7y-17)=0\Rightarrow x(3\lambda +1)+y(7\lambda +2)-(17\lambda +5)=0...\left(i\right)$
And this line is perpendicular to line 3x+4y=10
$\Rightarrow -\left(\frac{3\lambda +1}{7\lambda +2}\right)\left(\frac{-3}{4}\right)=-1\Rightarrow \lambda =-\frac{11}{37}$
On putting $\lambda$ in equation (i), we get
4x-3y+2=0