b = $\sqrt{2}$ cosθ         a = $\sqrt{2}$ sinθ
∴   C' $(\frac{\mathrm{cos\theta }}{\sqrt{2}},\frac{\mathrm{sin\theta }}{\sqrt{2}})$
x = 1 . cos(135° – θ) = $\frac{-\mathrm{cos\theta }}{\sqrt{2}}+\frac{1}{\sqrt{2}}\mathrm{sin\theta }$

          
Co-ordinate of orthocenter  = b + x = $\sqrt{2}$ cosθ – $\frac{\mathrm{cos\theta }+\mathrm{sin\theta }}{\sqrt{2}}$ = $\frac{\mathrm{cos\theta }+\mathrm{sin\theta }}{\sqrt{2}}$
y-co-ordinate of orthocenter = y₁ = 1 . sin(135° – θ)

       =  $\frac{\mathrm{cos\theta }}{\sqrt{2}}+\frac{1}{\sqrt{2}}\mathrm{sin\theta }$           
∴    ortho. $(\frac{\mathrm{cos\theta }+\mathrm{sin\theta }}{\sqrt{2}},\frac{\mathrm{cos\theta }+\mathrm{sin\theta }}{\sqrt{2}})$

        
∴    h =  $\frac{3\mathrm{cos\theta }+\mathrm{sin\theta }}{3\sqrt{2}}$      k =  $\frac{3\mathrm{cos\theta }+\mathrm{sin\theta }}{3\sqrt{2}}$
∴   cosθ = 3k$\sqrt{2}$ – 3sinθ
h =  $\frac{9(\mathrm{k}\sqrt{2}-\mathrm{sin\theta })+\mathrm{sin\theta }}{3\sqrt{2}}$
3$\sqrt{2}$ h = 9$\sqrt{2}$k – 8sinθ
sinθ =  $\frac{3\sqrt{2}(\mathrm{h}-3\mathrm{k})}{8}$    and     cosθ =  $\frac{3\sqrt{2}(\mathrm{k}-3\mathrm{h})}{8}$
∴  sin²θ + cos²θ = 1    (h – 3k)² + (k – 3h)² = $\frac{64}{9\times 2}$    (x – 3y)² + (y – 3x)² = $\frac{32}{9}$