![kennycooper3096](/avatars/12934.jpg)
kennycooper3096
09.01.2020 •
Mathematics
2. consider the circle x^2−4x+y^2+10y+13=0. there are two lines tangent to this circle having a slope of 2/3.
a. find the coordinates of the two points of tangency.
b. find the equations of the two tangent lines.
Solved
Show answers
More tips
- C Computers and Internet How to Teach Older Generations to Work with Computers?...
- L Leisure and Entertainment Unlocking the Secrets of Fast and Effective Tectonic Learning...
- S Style and Beauty How to Choose the Perfect Hair Color?...
- C Computers and Internet Best iPad Games: Our Opinion...
- A Animals and plants Man s Best Friend: Which Dog Breed Is the Most Friendly?...
- H Health and Medicine 10 Simple Techniques on How to Boost Your Mood...
- G Goods and services How to Choose the Right High Chair for Your Baby?...
- S Style and Beauty Learn how to tie a keffiyeh on your head like a pro...
- S Style and Beauty How to braid friendship bracelets?...
Answers on questions: Mathematics
- M Mathematics What is What is 99 / 10 + 2 3 / 5?...
- M Mathematics Can someone please tell me what the answer to Which equation shows how to use equivalent fractions to evaluate 3/4 +1/3 HURRY...
- M Mathematics 1. Choose the trig expression equal to the one below 2cos^2 x - 1...
- E English 11. Based on “Eleven, write an essay that explains Racheals view of herself and other characters in the story, and compare them to the readers view. (Eleven By Samantha Cisneros...
- M Mathematics How are chords and secants alike? How are they different?...
Ответ:
a) The coordinates are (0.431, -2.646) and (3.568,-7.354)
b) The tangent lines are
l₁ = (x-0.431)*2/3 - 2.646
l₂ = (x-3.568)2/3 - 7.354
Step-by-step explanation:
First, lets complete squares, by taking for each cordinate the square of a linear expression
0= x²−4x+y²+10y+13 = (x-2)²+ 4 + (y+5)²-25+13 = (x-2)²+(y+5)² - 8
Hence (x-2)² + (y+5)² = 8
Lets put y in function of x. We should obtain 2 functions f and g that represent the circle.
(y+5)² = 8 - (x-2)² = -x² + 4x + 4
Thus
Lets find the derivate of each function and the points in which they reach the value 2/3. In those points the tangent line will have a slope of 2/3.
We may just find the values of x which the derivate of f is either 2/3 or -2/3.
The quadratic has roots
one root is 3.568, which corresponds with g, and the other root is 0.431, corresponding to f.
Also g(3.568) = - 7.354 and f(0.431) = -2.646
This means that the coordinates are (0.431 , -2.646), (3.568 , -7.354) and the tangent lines are
l₁ = (x-0.431)*2/3 - 2.646
l₂ = (x-3.568)2/3 - 7.354
Ответ: