Mathematics - Point Question with Solution | TestHub

Solve line PQ \& QR Point $\mathrm{Q}\left(\frac{1-\mathrm{c}}{\mathrm{m}-1},\frac{1-\mathrm{c}}{\mathrm{m}-1}+1\right)$
$m_{2H}=\frac{\frac{1-c}{m-1}+2}{\frac{1-c}{m-1}-3}=\frac{1-c+2m-2}{1-c-3m+3}=-\frac{1}{4}$
${\mathrm{m}}_{2\mathrm{H}}=\frac{\frac{1-\mathrm{c}}{\mathrm{m}-1}+2}{\frac{1-\mathrm{c}}{\mathrm{m}-1}-3}=\frac{1-\mathrm{c}+2\mathrm{m}-2}{1-\mathrm{c}-3\mathrm{m}+3}=-\frac{1}{4}$...(1)
$\because {\mathrm{m}}_{\mathrm{PH}}=\frac{5}{0}\to \infty$
$\Rightarrow$ Slope of line QR (m) $=0$
Put value of $m$ in equation (1)
$\frac{1-c-2}{1-c+3}=-\frac{1}{4}\Rightarrow c=0$
so $\mathrm{m}-\mathrm{c}=0$ Ans.