Find the Path of a Heat-Seeking Particle Placed at Point $P ( 16,16 ) \text { on a metal plate }$

Multiple Choice

Find the path of a heat-seeking particle placed at point $P ( 16,16 ) \text { on a metal plate }$ with a temperature field $T ( x , y ) = 401 - 6 x ^ { 2 } - 3 y ^ { 2 }$ .

A) $y ^ { 2 } = 32 x$
B) $y ^ { 2 } = 32 x ^ { 2 }$
C) $y = 256 x ^ { 2 }$
D) $y ^ { 2 } = 16 x$
E) $y = 16 x ^ { 2 }$