Find the equation of the tangent to the curve which is parallel to the line 4x − 2y + 5 = 0.

It is given that

Then, the equation of the tangent at any given point (x, y) is given by,

The equation of the given line is 4x − 2y + 5 = 0

⇒ y = 2x +

⇒ slope of the line = 2

Now, the tangent to the given curve is parallel to the line 4x − 2y + 5 = 0

if the slope of the tangent = the slope of the line

When x =,

y =

Then, Equation of the tangent passing through the point is given by:

⇒ 24y – 18 = 48x – 41

⇒ 48x -24y =23

Therefore, the equation of the required tangent is 48x -24y =23