Question

$A=\left(2,5\right),B=\left(4,-11\right)$ and the locus of 'C' is $9x+7y+4=0$ Then the locus of the centroid of $\Delta ABC$ is

• A. $27x+21y-8=0$
• B. $3x+4y-2=0$
• C. $24x+22y-6=0$
• D. $5x+3y-7=0$

Answer 1

Answer: (A)

$27x+21y-8=0$

$\text{Given:}$

$A=(2,5),B=(4,-11)\text{and}$

$\text{focus of}c\text{is}9x+7y+40$

$\text{Let the x-cooridinate of}c\text{is}d$

$\text{so,}$

$9\alpha +7y+4=0$

$y=-\frac{9\alpha -4}{7}$

$x\text{-cooridinate of centriod is}$

$y=\frac{5-11-\frac{9\alpha -4}{7}}{3}$

$3y=-6+\left(\frac{-9(3x-6)-4}{7}\right)$

$21y=-42-27x+54-4$

$27x+21y+(-8)=0$

$27x+21y-8=0$

option $A$ is correct