Answer:
 y = 13*( -x/9 + 1/5)
Step-by-step explanation:
Given:
- The curve has an equation as follows:
                                
Find:
a. Verify that the given point (2,2) lies on the curve. 
b. Determine an equation of the line tangent to the curve at the given point.
Solution:
 - To verify whether the point lies on the given curve we will substitute the coordinates of the point into the equation as follows:
                               44 = 5*(2)^2 + 3*(2)(2) + 3*(2)^2
                               44 = 20 + 12 + 12
                               44 = 44 ......Hence proven.
- The equation of the line tangent to the curve is expressed as a linear function as follows:
                               y = m*x + C
Where, m is the gradient of the line.
             C is the y-intercept.
                               m = Δy / Δx = dy/dx
- We will take the derivative of the given curve with respect to x as follows:
                              
- Evaluate y' at the point (2,2) we get:
                             y' = - ( 10(2) + 3(2) ) / ( 3(2) + 6(2) )
                             y' = - ( 26 ) / (18)
                             y'= m = - 13/9 
- To evaluate C, we will use the point (2,2) for linear expression above with m as follows:
                             y = -13*x/9 + C 
                             2 =-13*(2)/9 + C
                             C = 13 / 5
- The equation of the tangent is as follows:
                             y = 13*( -x/9 + 1/5)