1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
irina [24]
3 years ago
12

Find the equation of the normal to the circle, whose equation is given below, at the point (1,2).( x − 3 ) 2 + ( y + 2 ) 2 = 20

Mathematics
1 answer:
grandymaker [24]3 years ago
8 0

Answer:

The equation of the normal is y = 4 - 2·x

Step-by-step explanation:

The given equation of the circle, is presented as follows;

(x - 3)² + (y + 2)² = 20

The point of the normal of the circle = (1, 2)

The equation of the normal to a circle, x² + y² + D·x + E·y + F = 0 at a point P(x₁, y₁) is given as follows;

\dfrac{y - y_1}{x - x_1} = \dfrac{2 \cdot y_1 + D}{2 \cdot x_1 + E}

Expanding the given equation of the circle, gives;

(x - 3)² + (y + 2)² = x² + y² - 6·x + 4·y + 13 = 20

∴ x² + y² - 6·x + 4·y + 13 - 20 = x² + y² - 6·x + 4·y - 7 = 0

x² + y² - 6·x + 4·y - 7 = 0

∴ x₁ = 1, y₁ = 2, D = -6, E = 4, and F = 13

Which gives;

\dfrac{y - 2}{x - 1} = \dfrac{2 \times 2 + 4}{2 \times  1 + (-6)} = \dfrac{8}{-4} = -2

∴ y - 2 = -2 × (x - 1) = 2 - 2·x

y = 2 - 2·x + 2 = 4 - 2·x

The equation of the normal to the circle with equation (x - 3)² + (y + 2)² = 20, at the point (1, 2) is y = 4 - 2·x

You might be interested in
The basis for an effective evaluation of art is the<br> _____ analysis of the artwork.
horsena [70]

Answer: Visual

Step-by-step explanation:

Visually analyzing the art work is an effective way

4 0
3 years ago
Josh has 40 minutes to complete a government exam. There are 15 multiple-choice questions worth 3 points each. There are also 5
Sauron [17]
Since there is no graph presented, I will give an example. For instance you are given, 2n is greater than 30 and 5n is less than 100 and you are asked to find the value of n. This is an example of an inequality problem. You are given 2n is greater than 30 and 5n is less than 100. You are asked to find for the value of n. You need to know that greater means this sign ‘>’ and lesser means ‘<’ sign. So if you have 2n is greater than 30, this is equal to 2n>30 and 5n is less than 100 is 5n<100. The ‘and’ means equal sign ‘=’. So,

2n>30+5n<100

2n-5n

<span> </span>

8 0
3 years ago
Quick help needed, need someone to check my answer.
Verdich [7]

The answer is B. 10 vertices because it all depends on the edges. You have to subtract the edges by faces/vertices to get your faces/vertices so 20-12 is 10 so you are correct

4 0
3 years ago
Logan saves $5.50 in dimes and quarters over a week. He has 20 more dimes than quarters. Find the number of dimes and quarters h
Sveta_85 [38]
10 quarters 30 dimes
7 0
3 years ago
Read 2 more answers
Simplify this expression: -2(-4x + 2y - 6)
Monica [59]

Answer:

8x - 4y + 12

Step-by-step explanation:

-2(-4x + 2y - 6)

(-2)(-4x) + (-2)(2y) + (-2)(-6)

(2 * 4x) - (2 * 2y) + (2 * 6)

8x - 4y + 12

4 0
2 years ago
Other questions:
  • Find the function y = f(t) passing through the point (0,12)
    13·1 answer
  • A commercial airplane travels 5,000 feet east and then ascends 3,000 feet from its starting point in the sky. Upon noticing a se
    14·1 answer
  • 1) If two angles have a sum of 180 degrees, what is the relationship<br> between them?*
    15·2 answers
  • The point (2, –4) is reflected across the line y = –1. What are the coordinates of the image?
    5·2 answers
  • Hi there, can anyone help me with this question?
    5·1 answer
  • 5×5×5×5×5×5<br><img src="https://tex.z-dn.net/?f=%20%7B5%7D%5E%7B6%7D%20" id="TexFormula1" title=" {5}^{6} " alt=" {5}^{6} " ali
    12·2 answers
  • What is the integer?
    8·1 answer
  • which equation represents a liner function that has a slope of 4/5 in the Y intercept of -6 y = -6x + 4/5 y = 4/5 x - 6y = 4/5 x
    7·2 answers
  • Cannn yalll help meee pweasee
    5·1 answer
  • (10 - 5) + 5^2 - 2 =
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!