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Ivahew [28]
3 years ago
5

#2 pls help I don’t know how to do math

Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
4 0

Answer:

3

Step-by-step explanation:

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Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). An equation of the tan
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2(x^2+y^2)^2=25(x^2-y^2)

Let y=y(x), so that differentiating both sides wrt x gives

4(x^2+y^2)\left(2x+2y\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(2x-2y\dfrac{\mathrm dy}{\mathrm dx}\right)

If x=-3 and y=1, the above reduces to

40\left(-6+2\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(-6-2\dfrac{\mathrm dy}{\mathrm dx}\right)\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac9{13}

This is the slope of the tangent line, which has equation

y-1=\dfrac9{13}(x+3)\implies\boxed{y=\dfrac{9x+40}{13}}

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3 years ago
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