What is the tangent of x^2=2y ?

The tangent of x^2=2y is y=a_{0}x+(a_{0}^2)/2-a_{0}^2

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tangent of x^2=2y

tangent of

x^{2} = 2 y

y = a_{0} x + \frac{a _{0}^{2}}{2} - a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0}^{2}}{2})

Find the slope of

x^{2} = 2 y : \frac{d y}{d x} = x

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = a_{0}

Find the line with slope m=

a_{0}

and passing through

(a_{0}, \frac{a _{0}^{2}}{2}) : y = a_{0} x + \frac{a _{0}^{2}}{2} - a_{0}^{2}

y = a_{0} x + \frac{a _{0}^{2}}{2} - a_{0}^{2}

What is the tangent of x^2=2y ?
The tangent of x^2=2y is y=a_{0}x+(a_{0}^2)/2-a_{0}^2