4. Find the equation of the normal to curve which passes through the point (1, 2).
Given the equation of the curve
We know that the slope of the tangent at a point on the given curve is given by
We know that
At point (a,b)
Now, the equation of normal with point (a,b) and
It is given that it also passes through the point (1,2)
Therefore,
-(i)
It also satisfies equation -(ii)
By comparing equation (i) and (ii)
Now, equation of normal with point (2,1) and slope = -1
Hence, equation of normal is x + y - 3 = 0