Question

if the line $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent, then the value of $\lambda$ is.

• A. 0
• B. 1
• C. -1
• D. 2

Answer 1

The correct option is D 2

We have,

Point of intersection of pair of lines represented by

$a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$

$is$$(\frac{hf-bg}{ab-h^2},\frac{gh-af}{ab-h^2})$

For the lines

$x^{2}2xy-35y^2-4x+44y-12=0$

$a=1,b=-35,h=1,g=-2,f=22,c=-12$

$\frac{hf-bg}{ab-h^2}=\frac{1\left(22\right)-(-35)(-2)}{1(-35)-1^2}=\frac{22-70}{-36}=\frac{-48}{-36}=\frac{4}{3}$

$\frac{gh-af}{ab-h^2}=\frac{(-2)\left(1\right)-\left(1\right)22}{1(-35)-1^2}=\frac{-24}{-36}=\frac{2}{3}$

$\text{point}\text{of}\text{intersection}=(\frac{4}{3},\frac{2}{3})$

$\text{the}\text{must}\text{satisfy}5x+\lambda y-8=0$

$5\left(\frac{4}{3}\right)+\lambda \left(\frac{2}{3}\right)-8=0$

$20+2\lambda -24=0$

$2\lambda =4$

$\lambda =2$

Hence, this is the answer.