The equation of chord of the parabola ${\mathrm{y}}^2=2\mathrm{x}$ having (1, 1) as its midpoint is

Given parabola

 $$\begin{gathered} {\mathrm{y}}^2=2\mathrm{x} \\ \mathrm{and} \mathrm{mid} \mathrm{point} \mathrm{of} \mathrm{chord} \mathrm{is} \left(1,1\right) \end{gathered}$$

Now equation  of chord  is ${\mathrm{S}}_1={\mathrm{S}}_{11}$

$$\begin{gathered} \left({\mathrm{yy}}_1-\left(\mathrm{x}+{\mathrm{x}}_1\right)\right)={{y_1}^2}_{ }-2x_1 \\ \Rightarrow y\left(1\right)-(x+1)=1-2 \\ \Rightarrow \mathrm{x}-\mathrm{y}=0 \end{gathered}$$