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dimaraw [331]
3 years ago
13

Write ellipse in standard form

Mathematics
1 answer:
irakobra [83]3 years ago
4 0
Ellipse in standard form
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Find the equation of a line tangent to the circle x2+(y−3)2=34 at the point (5, 0).
salantis [7]

Answer:

Step-by-step explanation:

In order to find the equation of the line tangent to that circle, we have to find the derivative by implicit differentiation which will give us the slope formula of that tangent line.  Let's begin by expanding through the parenthesis to get the standard form of the circle:

x^2+y^2-6y+9=34

Moving the 9 to the other side since the derivative of a constant is 0 gives us

x^2+y^2-6y=25

By implicit differentation, the derivative of that function is

2x+2y\frac{dy}{dx}-6\frac{dy}{dx}=0

To find the derivative, we have to solve for dy/dx:

2y\frac{dy}{dx}-6\frac{dy}{dx}=-2x

Factor out the dy/dx to get:

\frac{dy}{dx}(2y-6)=-2x

Now divide to get your slope formula (first derivative):

\frac{dy}{dx}=\frac{-2x}{2y-6}

Now we can sub in the x and y values from the coodinate to get the slope of that tangent line:

\frac{dy}{dx}=\frac{-2(5)}{2(0)-6}=\frac{-10}{-6}=\frac{5}{3}

So now that have the slope, we can use the point-slope form of a line to write the equation of the tangent line.  The point-slop form of a line is:

y-y₁ = m(x-x₁)

Filling in we get:

y - 0 = 5/3(x - 5) so the equation of the tangent line is:

y=\frac{5}{3}x-\frac{25}{3}

Good luck in your calculus class!

3 0
2 years ago
When are absolute values and the opposite of a rational number equal
miskamm [114]
When the rational number is negative
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Solve 9≤c+1. Graph the solution.<br><br> The solution is <br> .
hjlf
The answer to 9≤c+1 is c ≥ 8
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bazaltina [42]
<h3>Answer:</h3><h3>X = 10</h3>

Step-by-step explanation:

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In the diagram below, which pair of angles is complementary?
Nataly_w [17]

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/2 and /4 because angle 1 is 90

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