Question

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

Answer 1

The equation of the given curve is

The slope of the tangent to the given curve at any point (x, y) is given by,

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

4x − 2y + 5 = 0 ⇒ (which is of the form

∴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 is equal to the slope of the line.

∴Equation of the tangent passing through the point is given by,

Hence, the equation of the required tangent is.