Find the equation of the tangent line to the curve y = 2x² which is parallel to the line

First, let us find the slope of the given curve.

y = 2x²

Differentiating both sides, we get,

Given line: 4x – 2y + 5 = 0

2y = 4x + 5

Therefore, the slope of the line is 2.

The slope of the curve and slope of the line will be equal as both of them are parallel.

4x = 2

x = 1/2

Putting the value of x in a curve,

y = 1/2

Therefore, the point where we have to find equation of tangent is (1/2, 1/2)

Equation of tangent,

(y – 1/2) = 2(x – 1/2)

2y – 1 = 2(2x – 1)

2y – 1 = 4x – 2

Hence, the equation of tangent is 2y – 4x + 1 = 0.