Question -
Answer -
The equation of the given curve is y = x3 +2x + 6.
The slope of the tangent to the given curveat any point (x, y) is given by,
∴ Slope of the normal to the given curve at any point (x, y)=
The equation of the given line is x +14y + 4 = 0.
x +14y + 4 = 0 ⇒ 
(which is of the form y = mx + c)
∴Slope of the given line = 
If the normal is parallel to the line, then we must havethe slope of the normal being equal to the slope of the line.
When x = 2, y =8 + 4 + 6 = 18.
When x = −2, y =− 8 − 4 + 6 = −6.
Therefore, there are two normals to the given curvewith slopeand passing through the points (2, 18)
and (−2, −6).
Thus, the equation of the normal through (2, 18) isgiven by,And, the equation of the normal through (−2, −6) is givenby,
Hence, the equations of thenormals to the given curve (which are parallel to the given line) are
