The coordinates of a moving particle at any time are given by \[x=a{{t}^{2}}\] and \[y=b{{t}^{2}}\]. The speed of the particle at any moment is [DPMT 1984; CPMT 1997]

• A.             \[2t(a+b)\]      
• B.             \[2t\sqrt{({{a}^{2}}-{{b}^{2}})}\]
• C.             \[t\,\sqrt{{{a}^{2}}+{{b}^{2}}}\]          
• D.             \[2t\sqrt{({{a}^{2}}+{{b}^{2}})}\]