I will explain you and pair two of the equations as an example to you. Then, you must pair the others.
1) Two circles are concentric if they have the same center and different radii.
2) The equation of a circle with center xc, yc, and radius r is:
(x - xc)^2 + (y - yc)^2 = r^2.
So, if you have that equation you can inmediately tell the coordinates of the center and the radius of the circle.
3) You can transform the equations given in your picture to the form (x -xc)^2 + (y -yc)^2 = r2 by completing squares.
Example:
Equation: 3x^2 + 3y^2 + 12x - 6y - 21 = 0
rearrange: 3x^2 + 12x + 3y^2 - 6y = 21
extract common factor 3: 3 (x^2 + 4x) + 3(y^2 -2y) = 3*7
=> (x^2 + 4x) + (y^2 - 2y) = 7
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 7
=> (x + 2)^2 + (y - 1)^2 = 12 => center = (-2,1), r = √12.
equation: 4x^2 + 4y^2 + 16x - 8y - 308 = 0
rearrange: 4x^2 + 16x + 4y^2 - 8y = 308
common factor 4: 4 (x^2 + 4x) + 4(y^2 -8y) = 4*77
=> (x^2 + 4x) + (y^2 - 2y) = 77
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 77
=> (x + 2)^2 + (y - 1)^2 = 82 => center = (-2,1), r = √82
Therefore, you conclude that these two circumferences have the same center and differet r, so they are concentric.
Answer:
-5
Step-by-step explanation:
h(x) = -3x - 2
h(x) = 1
[ just put '1' in place of every 'x' ]
-3(1) -2
= -3 -2
= -5 (answer)
Answer:
Center (-2, 1), Radius 3
What is the distance from the midpoint of the circle to a point on the circle? It is 3 and not 9.
Example:
1. 2/3,3/4
<span>2. 3/5,1/2 </span>
<span>3. 2/5,1/3 </span>
<span>4. 5.6,4.5 </span>
<span>5. 1/2,2/3 </span>
<span>6. 3/7,2/3 </span>
<span>7. 1/3,3/10 </span>
<span>8. 2/5,3/7
</span>
Answer:
1. 8/12, 9/12
<span>2. 6/10, 5/10 </span>
<span>3. 6/15, 5/15 </span>
<span>4. 25/30, 24/30 </span>
<span>5. 3/6, 4/6 </span>
<span>6. 9/21, 14/21 </span>
<span>7. 10/30, 9/30 </span>
<span>8. 14/35, 15/35</span>
Answer:
1st angle = X
2nd angle = X + 7
3rd angle = X + 18
Then (sum. them): 3X + 25 = 180 ==> X = 51.67 degree
Therefore,
1st angle = 51.67 degree
2nd angle = 58.67 degree
3rd angle = 69.67 degree
