Find the equation of the tangent line at the given

erurnSopSoypegx

erurnSopSoypegx

Answered question

2021-12-02

Find the equation of the tangent line at the given point for the below curve.
x2y2=81;   (1,9)

Answer & Explanation

Lupe Kirkland

Lupe Kirkland

Beginner2021-12-03Added 21 answers

x2y2=81;   (1,9)
To find the tangent line equation, we first calculate dydx by implicit differentiation.
Differentiate with respect to x on both sides of the equation.
ddx(x2y2)=ddx(81)
2xy2+2x2ydydx=0 [chain and product rule]
2x2ydydx=2xy2
dydx=yx
To find the slope of the tangent line at the point (-1,9), let x=-1 and y=9. Then the slope is
m=91=9
Now the equation of the tangent line can be found by using the point-slope form of the equation of a line.
yy1=m(xx1)
y-9=9(x-(-1))
y=9+9x+9
y=9x+18
Result:
y=9x+18

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