Mathematics, 01.08.2019 12:40 wolfgirl10000

The tangent to the circle x^2+y^2=18 is parallel to the tangent x+y=6 what is the equation of the tangent?

Answers: 1

Show answers

Answers

Answer from: liliana74

y = -x - 6

Step-by-step explanation:

If we are looking for the equation of the line tangent to the circle, we have to find the first derivative of the circle function. If that tangent line is to be parallel to the given tangent line, we need to find the slope of the the given tangent line and make sure the slope of the line we are looking for is the same. First let's find the slope of the given tangent. If the given tangent is x+y=6, then to find the slope, solve for y:

y = -x + 6. So the slope of that line, and also the slope of the tangent we are solving for, is -1. Hold that thought while we find the derivative of the function. Using implicit differentiation, we find the derivative to be:

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

Solving for the slope (dy/dx) gives us:

$2y\frac{dy}{dx}=-2x$ and

$\frac{dy}{dx}=\frac{-2x}{2y}$ so

$\frac{dy}{dx}=-\frac{x}{y}$

Subbing in the value of the slope we found:

$-1=-\frac{x}{y}$ so

-y = -x or, equivalently,

y = x. Now that we know that y and x are the same value, we can go back to the original circle to find out what they both are by substitution. If y = x, we make the substution:

If x^2+y^2=18 , then

y^2+y^2=18 and

2y^2=18 and

y^2=9 so

y = ±3

We will choose the negative root (you'll see why in a second) and sub that in for both y and x since y and x are th same number. Going back to the fact that the slope is -1:

y - (-3) = -1(x - (-3)) simplifies a bit to:

y + 3 = -x - 3 which gives us, in slope-intercept form:

y = -x - 6

That is the equation of the tangent to the circle that is parallel to the given tangent.

If we would have chosen the principle (or positive) root of 3, our equation would have looked like this:

y - 3 = -1(x - 3) and

y = -x + 3 + 3 so

y = -x + 6. Notice that that is the EXACT SAME EQUATION as the given tangent. That's why we have to pick the negative 3 as our root.

Good luck in your calculus class! Make sure you post your questions in here! Many of us LOVE the challenge of calculus!

Answer from: Quest

i think this could be a possible answer (1 / 84) -1

good luck! : d

Answer from: Quest

rounding to the nearest thousandth would be 452,000

Another question on Mathematics

Mathematics, 21.06.2019 16:50

Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.

Answers: 3

Answer

Mathematics, 21.06.2019 19:10

At a kentucky friend chicken, a survey showed 2/3 of all people preferred skinless chicken over the regular chicken. if 2,400 people responded to the survey, how many people preferred regular chicken?

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

8. kelly wants to buy a magazine that is $25. later the magazine was marked up an additional 20%. what is the new price?

Answers: 1

Answer

Mathematics, 21.06.2019 21:50

Free points also plz look my profile and answer really stuff

Answers: 2

Answer

You know the right answer?

The tangent to the circle x^2+y^2=18 is parallel to the tangent x+y=6 what is the equation of the ta...