15) Find the equation of the tangent line to the curve which is (b) perpendicular to the line
Perpendicular to line means
We know that the equation of the line is
y = mx + c
on comparing with the given equation we get the slope of line m = 3 and c = 13/5
Now, we know that the slope of the tangent at a given point to given curve is given by
Given the equation of curve is
Now, when ,
Hence, the coordinates are
Now, the equation of tangent passing through (2,7) and with slope is
So,
Hence, equation of tangent is 36y + 12x = 227