Question
Asked Sep 30, 2019
32 at x 9
Let L be a tangent line to the hyperbola xy
Find the area of the triangle bounded by L and the coordinate axes
(Give your answer as a whole or exact number.)
A =
square units
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32 at x 9 Let L be a tangent line to the hyperbola xy Find the area of the triangle bounded by L and the coordinate axes (Give your answer as a whole or exact number.) A = square units

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Expert Answer

Step 1

We have to find slope at x=9

We need y'(9)

y'(9)= -32/81

ху%332
32
у3
32
у'3-
х?
32
У'9)-
92
32
У (9)-
81
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ху%332 32 у3 32 у'3- х? 32 У'9)- 92 32 У (9)- 81

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Step 2

At x=9, y=32/9

So we know slope= -32/81 and point is (9,32/9)

We will use the point slope formula to find the tangent

Tangent is y= (-32/81)x+(64/9)

32
-(x-9)
81
32
у-
9
32
32
X+
81
32
у-
9
9
32
X+
81
32
32
у--
9
9
32
64
-X+
81
9
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32 -(x-9) 81 32 у- 9 32 32 X+ 81 32 у- 9 9 32 X+ 81 32 32 у-- 9 9 32 64 -X+ 81 9

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Step 3

y intercept of the tangent is 64/9

To find x intercept w...

32
64
y= x+
-X+
81
9
64
32
81
32
64
X=
9
81
64 81
32
9
x 18
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32 64 y= x+ -X+ 81 9 64 32 81 32 64 X= 9 81 64 81 32 9 x 18

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