Mathematics - Circle Question with Solution | TestHub

We have $$\begin{array}{rl}& x^2+(8x)=9\\ & x^2+9x-x-9=0\\ & x(x+9)-1(x+9)=0\\ & (x+9)(x-1)=0\\ & x=-9,1\\ & \text{ for }x=1,y=\pm 2\sqrt{2x}=\pm 2\sqrt{2}\\ & {\mathrm{L}}_1=\text{ Length of }\mathrm{AB}\\ & =\sqrt{(2\sqrt{2}+2\sqrt{2}{)}^2+(1-1{)}^2}=4\sqrt{2}\\ & {\mathrm{L}}_2=\text{ Length of latus rectum }\\ & =4a=4\times 2=8\\ & {\mathrm{L}}_1<{\mathrm{L}}_2\end{array}$$