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میتونی لایو بذاری!

The equation of a curve is

${x^2} + 2xy - {y^2} + 8 = 0$

a) Show that the tangent to the curve at the point (−2, 2) is parallel to the x-axis.

b) Find the equation of the tangent to the curve at the other point on the curve for which $x =  - 2$, giving your answer in the form $y = mx + c$.

پاسخ تشریحی :
نمایش پاسخ

a) State $2y\frac{{dy}}{{dx}}$ as derivative of ${y^2}$, or equivalent

State $2y + 2x\frac{{dy}}{{dx}}$ as derivative of $2xy$, or equivalent

Substitute $x =  - 2$ and $y = 2$ and evaluate $\frac{{dy}}{{dx}}$

Obtain zero correctly and make correct conclusion

b) Substitute $x =  - 2$ into given equation and solve

Obtain $y =  - 6$ correctly

Obtain $\frac{{dy}}{{dx}} = 2$ correctly

Form the equation of the tangent at (–2, –6)

Obtain answer $y = 2x - 2$

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