Circle Equations Set #2
Rewrite the equation (x-2)² + (y + 1)² = 9 in general form.
x² + y² -4x+2y-4=0
Write the equation of a circle whose center is (-4, 8) and passes through the point (-2, -1).
(x + 4)² + (y - 8)² = 85
Create the equation of a circle in standard form given: C(-1 ½, 0) r = 2.5 units
(x+ 1.5)²+y² = 2.5² (x+ 1.5)²+y² = 6.25
Create the equation of a circle in standard form given: C(-8, -10) r=√5 units
(x+8)²+(y+10)² = 5
Create the equation of a circle in standard form given: C(2, -1) r=3 units
(x-2)²+(y+1)² = 9
Determine the center and radius given the equation of a circle is (x + 11.8)² + (y - 12.25)² = 27
Center (-11.8, 12.25) radius = √27 units
Determine the center and radius given the equation of a circle is (x + 7.46)² + (y + 9.41)² = ½
Center (-7.46, -9.41) radius √½
Determine the center and radius given the equation of a circle is x² + (y - 1)² = 4
Center (0, 1) radius = 2 units
Determine the center and radius given the equation of a circle is (x - 0.125)² + (y - 2.5)² = 144
Center (0.125, 2.5) radius= 12 units
Determine the center and radius given the equation of a circle is (x - 81)² + (y + 0.5)² = 16
Center (81, -0.5) r = 4 units
Rewrite the equation x² + y² + 8x + 2y = 9 in standard form.
Complete the square (x + 4)² + (y + 1)² = 14
Rewrite the equation x² + y² - 6x + 10y = 7 in standard form.
Complete the square (x - 3)² + (y + 5)² = 7 + 9 + 25 (x - 3)² + (y + 5)² = 41
Rewrite the equation x² + y² - 12x - 5y = 0.5 in standard form.
Complete the square x² -12x + y² - 5y = 0.5 x² -12x + 36 + y² - 5y + 6.25 = 0.5 + 36 +6.25 (x - 6)² + (y - 5/2)² = 42.75
A dog has dug a hole 5 miles east and 6 miles south of a tree to hide his toy. He will not move more than 4.5 miles away from his toy to ensure no one steals it. At that time, a squirrel tries to be sneaky and walk 0.5 miles east and 5 miles south away from the tree towards the dog's toy. If the squirrel does not move, does it make it onto the dog's territory, or is it still safe from being eaten? Explain your answer with a viable argument & justify with a mathematical approach.
Equation: (x-5)² + (y+6)² = 4.5² Squirrel: (0.5, -5) Substitute to get (-4.5)²+(1)²≠4.5² The squirrel is safe from being eaten because it does not make it into the dog's territory. The location of the squirrel does not fall on line of the circle.
A rabbit will move no more than 10 miles away from its hole. At that time, you are taking a walk about 6 miles west and 7 miles south of the rabbit hole. Is there any possibility of you meeting the rabbit?
Equation: x² + y² = 100 You: (-6, -7) Substitute to get 36+49≠100 There is no possibility of you meeting the rabbit because your location does not fall within the radius of the rabbit hole.
A radio tower services a 12 mile radius. You stop your car 8 miles east and 8 miles north of the tower. Will you be able to receive radio waves from the tower?
Equation: x² + y² = 144 You: (8, 8) Substitute to get 64+64≠144 No, you will not be able to receive radio waves from the tower because the location of the car is not within the radius of the radio waves.
Write the equation of a circle in standard form given that the center is (-1, 2) and a point on the circle is (2, 6).
Use distance formula to compute radius between center and point on circle. (x + 1)² + (y - 2)² = 25
Write the equation of a circle whose diameter has endpoints (4, -1) and (-6, 7).
Use the midpoint formula to find center: (-1, 3) Use distance formula to compute distance from center to ONE endpoint: √41 (x + 1)² + (y - 3)² = 41
Rewrite the equation x² + y² -4x + 2y - 4 = 0 in standard form.
You must complete the square to get (x-2)² + (y + 1)² = 9.
Create the equation of a circle in standard form given: C(0, 5) d = 16 units
diameter is 16 units, therefore radius is 8 units (x-0)²+(y-5)² = 8² x²+(y-5)² = 64
