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Dominik [7]
2 years ago
6

Find the equation of the tangent to the circle x2 + y2 = 109 at point (-10,3)

Mathematics
1 answer:
konstantin123 [22]2 years ago
4 0

Answer:

10x - 3y = -109 .

Step-by-step explanation:

x^2 + y^2 = 109

Implicit Differentiation:

2x + 2y.y' = 0

y' = -2x/2y = -x/y

So at the point (-10,3) the gradient of the tangent is -(-10)/3 = 10/3.

Equation of the tangent:

y - y1 = m(x - x1)

y - 3 = 10/3(x + 10)

y - 3 = 10/3 x + 100/3

3y - 9 = 10x + 100

-109 + 3y = 10x

10x - 3y = -109  

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Hi there!

The formula to find the are of a circle is :

a = \pir²

The formula to find the circumference of a circle is :

c = 2\pir


In order to use the area formula, you need to figure out what the radius (r) is.

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When we simplify this we get :

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Now you can put your value of "c" into this equation and find "a".

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Solving for "a" :

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28² = 28 × 28 = 784


a = 784 ÷ 4\pi


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a = 784 ÷ 12.56637061435917

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You need to round to the nearest square centimeter, which means that you need to round to the nearest whole number :

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