How do you calculate the gradient of tangent to xy=4 and x^2=16y?

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Answer 1 · 2018-07-11T08:32:30

At a point $(x_1,y_1)$ , the gradient is $-4/x_1^2$ , when it is on curve $xy=4$ and $x_1/8$ , when it is on $x^2=16y$ .

Gradient of a curve is given by the slope of curve at that point, whose value is value of the derivative at that point.

(1) Here $xy=4$ i.e. $y=4/x$ and $(dy)/(dx)=-4/x^2$ .

Now at point $(x_1,y_1)$ on the curve (observe $x_1y_1=4$ ),

the value of derivative of gradient of curve is $-4/x_1^2$

(1) Here $x^2=16y$ or $y=x^2/16$ and $(dy)/(dx)=x/8$ .

Now at point $(x_1,y_1)$ on the curve (observe $x_1^2=16y_1$ ),

the value of derivative of gradient of curve is $x_1/8$