A particle moves along a straight line to follow the equation\[a{{x}^{2}}+b{{v}^{2}}=k\], where\[a\], \[b\] and k are constants and \[x\] and \[v\] are x-coordinate and velocity of the particle respectively. Find the amplitude.

• A. \[\sqrt{\frac{k}{b}}\]                
• B. \[\sqrt{\frac{b}{k}}\]
• C. \[\sqrt{\frac{a}{k}}\]                
• D. \[\sqrt{\frac{k}{a}}\]