Find the equation of the normal lines to the curve which are parallel to the line .
Given: equation of the curve equation of line
To find: the equation of the normal lines to the given curve which are parallel to the given line
Explanation:
Now given equation of curve as
Differentiating the equation with respect to X
Assume the slope of the normal curve to be m2 is given by
Substituting value from equation (i), we get
The known equation of the line is
the slope of this line will be
since, slope of normal to the curve should be equal to the slope of the line which is parallel to the curve,
Substituting values from equation (ii) and (iii), we get
After putting y=x in the equation of the curve, we get
But from equation (iv)
y=x
Therefore, the points at which normal to the given curve is parallel to the given line are (2, 2) and (-2, -2)
Thus, the equations of the normal can be calculated by