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
Flura [38]
3 years ago
14

1.This circle is centered at the origin and contains the points two units away. Write the equation for this circle.

Mathematics
1 answer:
denis-greek [22]3 years ago
3 0

Answer:

1. The location of the center of the given circle = The origin (0, 0)

The given points on the circumference of the circle = (1, √3), and (0, -2)

The general form of the equation of a circle, is presented as follows

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

∴ (h, k) = (0, 0)

The radius of the given equation is the distance from the center (0, 0) to either the point (0, -2) or (1, √3)

The distance from the center (0, 0) to the point (0, -2), which are points on the same ordinate,  r = y₂ - y₁

∴ r =  0 - (-2) = 2

r = 2

The equation of the circle is therefore;

(x - 0)² + (y - 0)² = 2²

∴ x² + y² = 2²

2. When x = 1, and y = √3, we have;

(1 - 0)² + (√3 - 0)² = 1 + 3 = 4 = 2²

When x = 0, and y = -2, we have;

(0 - 0)² + ((-2) - 0)² = (-2)² = 4 = 2²

Therefore, the points shown on the circle (1, √3), and (0, -2) satisfy the equation of the circle, x² + y² = 2² and are solutions to the equation of the circle

Step-by-step explanation:

You might be interested in
What is the product of 84,90?
MAVERICK [17]
84•90 is 7,560.

ndheisn
3 0
3 years ago
Subtract (x^2+3x-4) -(4x-2x^2-3)
Feliz [49]

Answer:

3 x^2 - x + -1

Step-by-step explanation:

Simplify the following:

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

Factor -1 out of -2 x^2 + 4 x - 3:

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

(-1)^2 = 1:

2 x^2 - 4 x + 3 + x^2 + 3 x - 4

Grouping like terms, 2 x^2 + x^2 + 3 x - 4 x - 4 + 3 = (x^2 + 2 x^2) + (3 x - 4 x) + (-4 + 3):

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

x^2 + 2 x^2 = 3 x^2:

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

3 x - 4 x = -x:

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

3 - 4 = -1:

Answer: 3 x^2 - x + -1

4 0
3 years ago
About waves speed i want information about waves speed
Goryan [66]

Answer:

Wave speed is the distance that a wave travels in a given amount of time. Wave speed is related to wave length and wave frequency. Wave frequency can be found by using the formula Speed=wavelength × frequency

Step-by-step explanation:

6 0
3 years ago
When you square or cube a negative number is it still negative or does it become positive?
Fynjy0 [20]
When you square a negative number, the result is positive.
(-4)^2 = (-4)ª(-4) = 16

When you cube a negative number, the result is negative.
(-4)^3 = (-4)•(-4)•(-4) = -64

Negatives pair up and cancel out, so odd exponents always have one negative unpaired, making the result negative.
6 0
2 years ago
Which expression is equivalent to the expression below?
Annette [7]

Answer: B and D

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • Given the function rule f(x) = x² – 4x + 3, what is the output of f(–3)? (1 point)
    9·1 answer
  • Math graph equation. <br> (Picture.)
    13·1 answer
  • The sum of two numbers is 3. Their difference is -5. What are the two numbers?
    10·1 answer
  • For <img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%2B1" id="TexFormula1" title="f(x) = 4x+1" alt="f(x) = 4x+1" align="abs
    15·2 answers
  • Can someone help me ?
    9·1 answer
  • Text? I go to much going on inside of my head..
    13·1 answer
  • What is the nearest value of d to the nearest hundredth
    9·2 answers
  • Subtract -2/15 from -3/5 and add the result to 5/6​
    7·2 answers
  • - 7x-2y=-13<br> x - 2y = 1<br> Solve by substitution
    11·2 answers
  • Question : Explore criteria of congruency of triangles using a set of triangle cut outs
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!