53. The vertex and the axis of symmetry of the graph of \( y=x^{2}+5 \) are \( \begin{array}{ll}\text { a. }(5,0), x=5 & \text { b. }(0,-5), x=-5 \\ \text { c. }(-5,0), x=0 & \text { d. }\end{array} \)

12.3 The equations \( x^{2}+a x+b=0 \) and \( x^{2}+b x+a=0 \) both have real and equal roots. Solve for \( a \) and \( b \), where \( a>0 \) and \( b>0 \).

If \( x-6=0 \) is one of the solutions of the equation \( x+\frac{40}{x}=16 \), determine ONE value of \( y \) for which \( 2 y+3+\frac{40}{2 y+3}=16 \)

15. \( 5 x^{2}-47 x=156 \)

If \( x-6=0 \) is one of the solutions df the equation \( x+\frac{40}{x}=16 \), determine ONE value of \( y \) for which \( 2 y+3+\frac{40}{2 y+3}=16 \)

\( -\frac{1}{2 x}-\frac{1}{y}=-1 \) and \( \frac{1}{x}+\frac{1}{2 y}=8 \)