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
Luden [163]
3 years ago
11

Write the equation of the circle in general form. Show all of your work

Mathematics
2 answers:
finlep [7]3 years ago
8 0
<h2>1. What are the center and equation of the circle?</h2>

In this exercise we have the general form of the equation of a circle, which is given by:

x^2+y^2+18x+4y+49=0

The ordinary equation of a circle is:

(x-h)^2+(y-k)^2=r^2 \\ \\ Developing \ this \ equation: \\ \\ x^2+y^2-2hk-2ky+h^2+k^2-r^2=0

But this can be written as:

x^2+y^2+Dx+Ey+F=0 \\ \\ D=-2h, \ E=-2k, \ and \ F=h^2+k^2-r^2

From the original equation we know that:

D=18, \ E=4, \ and \ F=49 \\ \\ So: \\ \\ h=-\frac{18}{2}=9, \ k=-\frac{4}{2}=2, \ and \ r=\sqrt{9^2+2^2-49}=6

Finally:

\boxed{CENTER: \ (h,k)=(9,2)} \\ \\ \boxed{RADIUS: \ 6}

<h2>2. Write the equation of the circle in general form.</h2>

We need to write this equation in the form:

x^2+y^2+Dx+Ey+F=0

Since:

D=-2h, \ E=-2k, \ and \ F=h^2+k^2-r^2

Then we need to find the center and radius in order to get D, E and F then. From the graph, it is easy to know that the center is (h,k)=(-3,4) and the radius is 2. Therefore:

D=-2(-3)=6, \ E=-2(4)=-8, \ and \ F=(-3)^2+(4)^2-(2)^2=21

Finally, the general form of the equation is:

\boxed{x^2+y^2+6x-8y+21=0}

<h2>3. Write the equation of the parabola</h2>

A parabola is the set of all points in a plane that are equidistant from  a fixed line called the directrix and a fixed point called the focus that does not lie on the line. Since the directrix is x=2 then this is a horizontal axis. So the standard for of the equation of a parabola that matches this form is:

(y-k)^2=4p(x-h) \ \ p \neq 0

The vertex is (h,k)=(-5,8) so our goal is to find p:

(y-8)^2=4p(x+5)

We can find the absolute value of p as follows:

\left|p\right|=2-(-5)=7

Since the directrix is to the left of the vertex, the parabola opens to the left and hence:

p.

Finally, the equation is:

(y-8)^2=4(-7)(x+5) \\ \\ \boxed{(y-8)^2=-28(x+5)}

Assoli18 [71]3 years ago
4 0

Answer: The answer is x^2 + y^2 + 6x - 8y + 21 = 0.

Step-by-step explanation:

First find the original standard form equation of the circle.

So the circle has a center of (-3, 4) and a radius of 2. Write this in standard form:

(x + 3)^2 + (y - 4)^2 = 2^2

Simplify:

(x + 3)^2 + (y - 4)^2 = 4

(x^2 + 6x + 9) + (y^2 - 8y + 16) = 4

Gather like terms:

x^2 + y^2 + 6x - 8y + 9 + 16 - 4 = 0

x^2 + y^2 + 6x - 8y + 21 = 0

There you go!

You might be interested in
How do you solve this ?
Inga [223]
2.) y = x - 12

3.) 2x + 6

6 0
3 years ago
-2(3x-4)=4(5x-11) Solve for x
sveta [45]

-2(3x-4)=4(5x-11)

-6x+8=20x-44

8+44=26x

26x=52

x=52/26

your answer will be x=2

6 0
3 years ago
Read 2 more answers
Arjun has to stick by his budget. his salary is $112,000 after taxes. he divides his
geniusboy [140]
I hope this helps you :)

6 0
3 years ago
The Hu family goes out for lunch, and the price of the meal is $59. The sales tax on the meal is 7%, and the family also leaves
Setler79 [48]
$71.98 is the total cost for the meal
  59.00
+  4.13
+  8.85
======
  71.98
7 0
3 years ago
-6x – 29 = 5x – 7<br> What answer
zalisa [80]

Answer:

x=-2

Step-by-step explanation: :)

3 0
3 years ago
Read 2 more answers
Other questions:
  • Approximate √52 to the tenths place
    15·2 answers
  • HELPPPP PLEASEEEEEEEEE
    9·2 answers
  • points given to anyone even if you dont have right answer.(:your welcome.but still try to answer it Lol​
    5·1 answer
  • A sphere has a diameter of 4(x+3) centimeters and a surface area of 784π square centimeters. Find the value of x.
    9·1 answer
  • What is the slope of the line below
    7·1 answer
  • Find the circumference of the circle with 1/4 Pi square centimetre square 2<br>​
    12·1 answer
  • Solve for g. -7g − 8 = -6g
    7·1 answer
  • One number is one-third a second number. if the sum of the numbers is 48, find the numbers.
    8·1 answer
  • A 0.0375<br><br>B 6<br><br>C 60<br><br>D 600<br><br><br><br><br><br>Can you help pleaseeee!!
    5·1 answer
  • I NEEEDDD HELPPP!!! someone please help me outttt
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!