Find an equation of the tangent line to the graph of the function given below at the given point. $7 x ^ { 2 } - 2 x y + 4 y ^ { 2 } - 36 = 0 , \quad ( 2 , - 1 )$ (The coefficients below are given to two decimal places.)
A) $y = 7.50 x + 16.00$
B) $y = 2.50 x + 16.00$
C) $y = 2.50 x - 6.00$
D) $y = - 2.50 x - 6.00$
E) $y = 7.50 x - 16.00$

Question

Quizplus · Accepted Answer

To find the tangent line, we first need to find the derivative using implicit differentiation. Differentiating the given equation with respect to $x$ and evaluating at the point $(2, -1)$, we find the slope of the tangent line to be 2.5. Using the point-slope form of a line, the equation of the tangent line is $y = 2.50x - 6.00$.

Find an Equation of the Tangent Line to the Graph 7x2−2xy+4y2−36=0,(2,−1)7 x ^ { 2 } - 2 x y + 4 y ^ { 2 } - 36 = 0 , \quad ( 2 , - 1 )7x2−2xy+4y2−36=0,(2,−1)

Find an Equation of the Tangent Line to the Graph $7 x ^ { 2 } - 2 x y + 4 y ^ { 2 } - 36 = 0 , \quad ( 2 , - 1 )$