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
Sergeu [11.5K]
3 years ago
7

What is the equation for a circle with a center at (-2,-4) that passes through the point (3,8)?

Mathematics
2 answers:
Schach [20]3 years ago
5 0

Answer:

(x+2)²+(y+4)²=169

Step-by-step explanation:

In simplest terms

Margarita [4]3 years ago
3 0
Check the picture below.

so, the center of the circle is the midpoint of that diametrical segment, and half that length is the radius.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~ -2 &,& -4~) 
%  (c,d)
&&(~ 3 &,& 8~)
\end{array}\qquad
%   coordinates of midpoint 
\left(\cfrac{ x_2 +  x_1}{2}\quad ,\quad \cfrac{ y_2 +  y_1}{2} \right)
\\\\\\
\left( \cfrac{3-2}{2}~~,~~\cfrac{8-4}{2} \right)\implies \left( \frac{1}{2}~,~2 \right)\impliedby center

\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~ -2 &,& -4~) 
%  (c,d)
&&(~ 3 &,& 8~)
\end{array}~~~ 
%  distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{[3-(-2)]^2+[8-(-4)]^2}\implies d=\sqrt{(3+2)^2+(8+4)^2}
\\\\\\
d=\sqrt{25+144}\implies d=\sqrt{169}\implies d=13\qquad\qquad \qquad  \stackrel{radius}{\frac{13}{2}}

\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{\frac{1}{2}}{ h},\stackrel{2}{ k})\qquad \qquad 
radius=\stackrel{\frac{13}{2}}{ r}
\\\\\\
\left( x-\frac{1}{2} \right)^2+(y-2)^2=\left( \frac{13}{2} \right)^2\implies \left( x-\frac{1}{2} \right)^2+(y-2)^2=\frac{169}{4}

You might be interested in
A median is a segment that extends from the _____ of a triangle to the midpoint of the opposite side.
IRISSAK [1]

Answer:

Vertex.

Step-by-step explanation:

There are 3 medians in a triangle.

4 0
2 years ago
Read 2 more answers
A machine can stamp 40 envelopes in 8 minutes. How many of these machines, working simultaneously, are required or needed to sta
ziro4ka [17]

Divide 40 by 8 minutes to find the quantity per minute for one machine:

40 / 8 = 5 per minute.

One machine does 5 envelopes per minute.

Now divide 120 by 5 to find the number of machines needed:

120 / 5 = 24

24 machines would be needed.

8 0
3 years ago
Factorise 5n + 15<br> Please
White raven [17]

Answer:

The correct answer is

<u>5(n + 3)</u>

Use the distributive property to factor

Hope this helps!

- Quinn

4 0
3 years ago
Read 2 more answers
What this simplified
kati45 [8]

Answer:

\frac{3b\sqrt[3]{c^{2}} }{a^{2} }

Step-by-step explanation:

∛(27a⁻⁶b³c²)

To simplify, first apply the cube root the each of the terms. Keep in mind this rule: \sqrt[n]{a^{m}}  = (\sqrt[n]{a})^{m} = a^{m/n}

∛27 = 3    (because 3*3*3 = 27)

∛a⁻⁶ = a^{-6/3} = a^{-2} = \frac{1}{a^{2}}

∛b³ = b^{3/3} = b^{1} = b

∛c² = c^{2/3}

∛(27a⁻⁶b³c²)

= \frac{3b\sqrt[3]{c^{2}} }{a^{2} }

Simplified form generally follows these rules:

No negative exponents

No fraction exponents

Keep in fractional form

Reduce numerical values

5 0
3 years ago
The fifth graders were given sandwiches for lunch during their field trip. Nathan ate 5/6 of his sandwich, Leroy ate 7/8 of his
riadik2000 [5.3K]
Nathan ate 20/24, Leroy ate 21/24, and Sofia ate 15/24 meaning Leroy ate the most
4 0
3 years ago
Read 2 more answers
Other questions:
  • The expression x4 + 6x3 – 11x2 – 60x + 100 is equivalent to (x – 2)(x – 2)(x + 5)(x + 5). At what points does the graph of the f
    6·2 answers
  • Jerry is making a strawberry smoothie. which measure is greatest, the amount of milk, cottage cheese, or strawberries?
    10·1 answer
  • 6. Protein bars come in a 4-pack box or 12-pack
    10·1 answer
  • Ive got a big maths test tomorrow ask me questions on fractions or percentages , formula , significant figures , Pythagoras anyt
    9·1 answer
  • What is the 5th term in the sequence d(n)=5/16 (2)^n−1
    14·1 answer
  • A bed is 6 1/2 feet long.the material to make a sheet for the bed is to be 1 1/2 times as long to allow for hems and tucking und
    7·1 answer
  • PLS HELP ASAP! GIVING BRAINLY
    7·2 answers
  • Which ordered pair is a solution of this equation y = 80 – 8x?​
    9·1 answer
  • 4. The length of a rectangle is 4 more than its width. The perimeter of the rectangle is 60cm.
    12·1 answer
  • Conjunction and disconjuction​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!