Mathematics - Straight Lines Question with Solution | TestHub

Let $P(a,0)$ and $Q(0,b)$ slope of $PQ=\frac{-b}{a}$. Now $-\frac{b}{a}\times \frac{5}{7}=-1\Rightarrow \frac{a}{b}=\frac{5}{7}$

Equation of AQ is $\frac{x}{7}+\frac{y}{b}=1\Rightarrow b=\frac{7y}{7-x}$

Equation of BP is $\frac{x}{a}-\frac{y}{5}=1\Rightarrow a=\frac{5x}{5+y}$

So that $\frac{5x}{5+y}\times \frac{7-x}{7y}=\frac{a}{b}=\frac{5}{7}\Rightarrow x(7-x)=y(5+y)$

$\Rightarrow x^2+y^2-7x+5y=0$

which is the locus of $R(x,y)$