a$.$ Verify that the given point lies on the curve.

b$.$ Determine an equation of the line tangent to the curve at the given point.

$6x^{2}6xy3y^2=39$;$(2,1)$

a$.$ Verify that the point is on the given curve.

It is given that the right side of the equation equals $39.$ Evaluate the left side, $6x^{2}6xy3y^2,$ when $x$ is $2$ and y is $1.$

When $x$ is $2$ and $y$ is $1,6x^{2}6xy3y^2=($Simplify your answer.$)$

Does the point lie on the curve $6x^{2}6xy3y^2=39?$

A$.$ No$,$ because the point $(2,1)$ is in the domain of the implicit function.

B$.$ No$,$ because the value of $6x^{2}6xy3y^2$ does not equal $39$ when $x$ is $2$ and $y$ is $1.$

C$.$ Yes, because the point $(2,1)$ is in the first quadrant.

D$.$ Yes, because the value of $6x^{2}6xy3y^2$ is $39$ when $x$ is $2$ and $y$ is $1.$b$.$ Write the equation for the tangent line in slope$-$intercept form. Select the correct choice and, if necessary, fill in the answer box to complete your choice.

A$.$ The point $(2,1)$ lies on the curve. The equation of the tangent line is $y=($Use integers or fractions for any numbers in the equation.$)$

B$.$ The point $(2,1)$ does not lie on the curve.