Mathematics, 15.07.2019 15:30 daydallas01

Find an equation of the tangent line to the hyperbola y = 3/x at the point (3, 1).

Answers: 1

Show answers

Answers

Answer from: juanmias

The equation of the line tangent to the hyperbola at the point (3,1) is $y = -\frac{1}{3}\cdot x + 2$ .

Procedure - Determination of a line tangent to a hyperbola

By analytical geometry we know that tangent lines are described by the line equation:

$y = m\cdot x + b$ (1)

Where:

- Independent variable.

- Slope.

- Intercept.

- Dependent variable.

By calculus we know that the slope of the tangent line is defined by the first derivative of the hyperbola evaluated at point of tangence:

$m = -\frac{3}{x^{2}}$ (2)

If we know that x = 3 and y = 1 , then the equation of the tangent line is:

Slope

$m = -\frac{1}{3}$

Intercept

$b = 1-\left(-\frac{1}{3} \right)\cdot (3)$

b = 2

The equation of the line tangent to the hyperbola at the point (3,1) is $y = -\frac{1}{3}\cdot x + 2$ . $\blacksquare$

To learn more on tangent lines, we kindly invite to check this verified question: link

Answer from: lillyd2873

Let's find the derivative of that hyperbola in order to find a slope formula to help us with this equation. We already have an x and y value. The derivative is found this way: $y'= \frac{x(0)-3(1)}{x^2}$ so $y'=- \frac{3}{x^2}$ . The derivative supplies us with the slope formula we need to write the equation. Sub in the x value of 3 to find what the slope is: $y'=- \frac{3}{3^2}=- \frac{3}{9}=- \frac{1}{3}$ . So in our slope-intercept equation, x = 3, y = 1, and m = -1/3. Use these values to solve for b. $1=- \frac{1}{3}(3)+b$ so b = 2. The equation, then, for the line tangent to that hyperbola at that given point is $y=- \frac{1}{3}x+2$

Answer from: Quest

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒ $y=\frac{+1}{+1}x+0$

or $y=\frac{-1}{-1}x+0$

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

Answer from: Quest

what is the information provided?

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 20:10

21 type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. the solution set of n2 - 14n = -45 is { (separate the solutions with a comma)

Answers: 3

Answer

Mathematics, 21.06.2019 21:30

Madeline takes her family on a boat ride. going through york canal, she drives 6 miles in 10 minutes. later on as she crosses stover lake, she drives 30 minutes at the same average speed. which statement about the distances is true?

Answers: 3

Answer

Mathematics, 22.06.2019 00:20

The police chief wants to know if the city’s african americans feel that the police are doing a good job. identify the management problem (i.e dependent variable) and identify the independent variable.

Answers: 1

Answer

Mathematics, 22.06.2019 01:50

Me asap the graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants according to the line of best fit about how many ounces of frozen yogurt can someone purchase for $5? 1 cost of frozen yogurt 1.5 2 13 15.5 cost (5) no 2 4 6 8 10 12 14 16 18 20 size (oz)

Answers: 1

Answer

You know the right answer?

Find an equation of the tangent line to the hyperbola y = 3/x at the point (3, 1)....

Questions