60–62. {Use of Tech} Multiple tangent lines Complete the following steps. <IMAGE>
a. Find equations of all lines tangent to the curve at the given value of x.
4x³ =y²(4−x); x=2 (cissoid of Diocles)​​

Verified step by step guidance

1. First, differentiate the given equation of the curve, which is 4x³ = y²(4 - x), with respect to x to find the slope of the tangent line at any point on the curve.
2. Next, substitute x = 2 into the original equation to find the corresponding y-coordinate(s) on the curve.
3. After finding the y-coordinate(s), use the derivative obtained in step 1 to evaluate the slope of the tangent line at the point(s) (2, y).
4. With the slope and the point(s) (2, y) determined, apply the point-slope form of the equation of a line, which is y - y₁ = m(x - x₁), to find the equation(s) of the tangent line(s).
5. Finally, simplify the equation(s) of the tangent line(s) to express them in slope-intercept form or standard form as required.