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
liraira [26]
3 years ago
14

Write the standard form of the equation of the circle that passes through the point

Mathematics
1 answer:
AnnZ [28]3 years ago
5 0

Answer:

The standard form of the equation of the circle is x^2+y^2=1.

Step-by-step explanation:

A circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center.

The equation of a circle in standard form is

                                             (x-h)^2+(y-k)^2=r^2

where <em>r</em> is the radius of the circle,  and <em>h</em>, <em>k</em> are the coordinates of its center.

When the center of the circle coincides with the origin h=k=0, so

                                            (x-0)^2+(y-0)^2=r^2\\x^2+y^2=r^2

We are also told that the circle contains the point  (0, 1), so we will use that information to find the radius <em>r</em>.

                                                   0^2+1^2=r^2\\r^2=0^2+1^2\\r^2=1\\r=\sqrt{1}

Therefore, the standard form of the equation of the circle is x^2+y^2=1.

You might be interested in
How many distinct products can be formed using two different integers from the given set: {–6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4
zhannawk [14.2K]

Number of distinct products that can be formed is 144

<h3>Permutation</h3>

Since we need to multiply two different integers to be selected from the set which contains a total of 12 integers. This is a permutation problem since we require distinct integers.

Now, for the first integer to be selected for the product, since we have 12 integers, it is to be arranged in 1 way. So, the permutation is ¹²P₁ = 12

For the second integer, we also have 12 integers to choose from to be arranged in 1 way. So, the permutation is ¹²P₁  = 12.

<h3>Number of distinct products</h3>

So, the number of distinct products that can be formed from these two integers are ¹²P₁ × ¹²P₁ = 12 × 12 = 144

So, the number of distinct products that can be formed is 144

Learn more about permutation here:

brainly.com/question/25925367

6 0
2 years ago
Three times the sum of a number and seven is two less than five times the number.
m_a_m_a [10]
3 (x + 7) =  5x - 2
3x + 21 = 5x - 2
3x - 5x = -2 - 21

-2x = -23 
x = -23/-2
x = 23/2


4 0
2 years ago
Point a pq and r are collinear on pr and pq: pr =2/3. P is located on the origin q is located at (x,y) and r is located at (-12,
dybincka [34]

The values of x and y are  8 and 0 respectively.

<em><u>Explanation</u></em>

As 'p' is located at (0,0) and 'r'  is located at (-12,0) , that means both 'p' and 'r' are on the x-axis.  So point 'q' will be also on the x-axis , and 'q' is located at (x,y)

So, the value of y will be 0. That means the co ordinate of point 'q' is (x, 0)

Now, using the Distance formula, length of 'pq' = \sqrt{(x-0)^2 +(0-0)^2}= \sqrt{x^2}= x

and length of  'pr'  = \sqrt{(-12-0)^2+(0-0)^2}= \sqrt{144}=12

Given that,   pq : pr =2/3

So....

\frac{x}{12} =\frac{2}{3}\\ \\ 3x=24\\ \\ x= \frac{24}{3}=8

Thus, the values of x and y are  8 and 0 respectively.

8 0
3 years ago
Triangle RST has vertices located at R (2,3), S (4,4), and T (5,0).
Mazyrski [523]

The slope of RS, RT, and ST are 1/2, -1 and -4 respectively

<h3>Triangle and slopes</h3>

Given the folllowing coordinates R (2,3), S (4,4), and T (5,0) os triangle RST

The formula for calculating the distance is expressed as:

  • D = √(x2-x1)²+(y2-y1)²

For length RS:

D = √(4-3)²+(4-2)²

RS = √1+4
RS= √5

For length RS:

RT = √(0-3)²+(5-2)²

RT = √9+9
RT= 3√2

For length ST:

D = √(0-4)²+(5-4)²

ST = √16+1
ST= √17

Since all the sides are different, the triangle is a scalene triangle.

For the slope of the sides

For the side RS;

Slope = 4-3/4-2

Slope of RS = 1/2

For the side RT:

Slope = 0-3/5-2

Slope of RT = -3/3 = -1

For the side ST

Slope of ST = 0-4/5-4
Slope of ST = -4/1 = -4

Hence the slope of RS, RT, and ST are 1/2, -1 and -4 respectively

Learn more on slope and distance here: brainly.com/question/2010229

6 0
2 years ago
Solve |x + 4| - 5 =6.
dedylja [7]

Answer:

The answer is x =7 and x= - 15

<em>Explanation</em>

|x + 4|  - 5 = 6 \\  |x + 4|  = 6 + 5 \\  |x + 4|  = 11 \\ x + 4 = 11  \: \:and \:  \: x + 4 =  - 11 \\ x = 11 - 4 \:  \: and \:  \: x =  - 11 - 4 \\ x = 7 \: \:  and \:  \: x =  - 15

4 0
3 years ago
Other questions:
  • If you had to put up a fence around a circular baseball field, you would need to know the _________? Area Diameter Circumference
    6·2 answers
  • On a True/False test, Amy answered the first three questions wrong but answered the rest of the questions correctly. On the same
    12·1 answer
  • Do, 2(x, y)+(3,5).<br> The point (x, y) is<br> (1,3)<br> (-3/2, -5/2)<br> (-6, -10)
    11·1 answer
  • <img src="https://tex.z-dn.net/?f=%28fog%29%28%20-%205%29" id="TexFormula1" title="(fog)( - 5)" alt="(fog)( - 5)" align="absmidd
    9·1 answer
  • Mr. Shirey is baking cookies to sell for a charity. He bakes 12 dozen cookies in 4 hours. How many cookies
    9·2 answers
  • The probability of breaking a window while playing baseball in the backyard is 0.78. What is the likelihood that a window will b
    5·1 answer
  • how do I solve subtract 19 from My number and mulitply the difference by -4 , the result is -44 What is Sara number​
    14·1 answer
  • Use slopes and y-intercepts to determine if the lines y=−2/3x+2 and −3x+2y=−4 are parallel.
    7·1 answer
  • Y=1/3 x-4 system of equations
    5·2 answers
  • What is the completely factored form of p4 – 16? (p – 2)(p – 2)(p 2)(p 2) (p – 2)(p – 2)(p – 2)(p – 2) (p minus 2) (p 2) (p squa
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!