​please answer this

​please answer this Question 58 of 90 Find the slope of the tangent line to the curve that is the intersection of the surface z = x2 —Y2 with the plane x at the point (2, 1 3). 1/2

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ \mathrm{f}\left(\mathrm{x},\mathrm{y}\right)={\mathrm{x}}^2-{\mathrm{y}}^2 \\ \frac{\partial \mathrm{f}}{\partial \mathrm{y}}\left(2,\mathrm{y}\right)=\frac{\partial \mathrm{f}}{\partial \mathrm{y}}\left(2^2-{\mathrm{y}}^2\right)=-2\mathrm{y} \\ \mathrm{Hence} \mathrm{slope} \mathrm{at} \left(2,1,3\right) \mathrm{is} -2\times 1=-2 \left[\mathrm{Answer}\right] \end{gathered}$$

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