Find the equation of normal at point (a, a) of the curve xy = `a^(2)`.

Explanation

`xy = a^(2)`
`rArr x* ((dy)/(dx)) + y*1=0`
`rArr ((dy)/(dx)) =-y/x`
At point (a, a), the slope of tangent `m_(1) = ((dy)/(dx))_"(a,a)"`
`=(-a)/a =-1`
`rArr` Slope of normal at point (a, a)
` m_(2) =-1/(m_(1) = 1`
`:. ` Equation of normal at point (a, a)
` y-a=1 (x-a)`
` rArr x- y =0`.