Find an equation of the tangent line to the curve $120 \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 2312 \left( x ^ { 2 } - y ^ { 2 } \right)$ at the point $( 4,1 )$.
A) $y = - 1.11 x + 17$
B) $y = - 1.11 x + 3.43$
C) $y = 1.11 x + 5.43$
D) $y = - 1.11 x + 5.43$
E) None of these

Question

Quizplus · Accepted Answer

To find the tangent line, first implicitly differentiate the given equation with respect to $x$. Then, substitute $x = 4$ and $y = 1$ into the differentiated equation to find the slope of the tangent line. Finally, use the point-slope form of a line to find the equation of the tangent line. The correct equation is $y = -1.11x + 5.43$.

Find an Equation of the Tangent Line to the Curve 120(x2+y2)2=2312(x2−y2)120 \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 2312 \left( x ^ { 2 } - y ^ { 2 } \right)120(x2+y2)2=2312(x2−y2)

Find an Equation of the Tangent Line to the Curve $120 \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 2312 \left( x ^ { 2 } - y ^ { 2 } \right)$