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Standard equation of a circle
U10L9 Standard Form of a Circle Solutions H
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Name: Date: Per: ** This is a 2-page document! ** Directions: Graph each circle and identify its center and radius. 1. (x-6)² + (y− 1)² = 9 2. (x-2)²+(y + 3)² = 36 3. x² + (y + 2)² = 64 Center: (6,1) Radius: 3 Unit 10: Circles Homework 9: Standard Form of a Circle Center: (0,-2) Radius: 8 4. (x+4)² + (y−5)² = 25 Directions: Identify each part of the circle given its equation. 5. (x-9)²+(y-4)² = 400 Center: (9,4) 6. (x + 1)² + (y−1)² = 256 7. (x+6)² + y² = 90.25 8. (x-2)²+(y+13)² = 150 9. (x+7)² + (y+4)² = 16 10. (x-10)²+(y-5)² = 28 11. x² + (y + 3)² = 81 12. (x + 5)² + (y-2)² = 135 Center: (1.1) Center: (-6,0) Center: (2,-13) Center: (-1,-4) Radius: 2 Center: (0₁-3) Diameter: S Center: (2,-3) Radius: 6 Center: (-4,5) Radius: 5 Radius: 20 Diameter: 32 Diameter: 19 Radius: 5√6 Circumference: 8TT (25.1) Circumference: 4√7 (332) Area: 81 TT (254.5) Area: 135T (424.1) Ⓒ Gina Wilson (All Things Algebra, LLC), 2015-2019 Write each equation in standard form. Then identify each part. 13. x² + y² +8x-6y-25-0 x²+8x + y²-6y = 25 x ²4x + y²-12y = 129 x² +8x + 16 + y²-6y + 9 = 25+16+1| x² - 4x + 4 + y²-12y + 36 = (x+4)² + (y-3)² = 50 129 +4+36 Standard Form: (x+4)² + (y-3)² = 50 Center: (-4,3) Radius: 5√2 15. x² + y² +14x+10y + 73 = 0 x²+14x+y²+10y=-13 x² +14x +49 + y² +10y + 25 (x+1)² + (y + 5)² = 1 Standard Form: -73 +49...
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Alternative transcript:.
+25 (x+7)² + (y + 5)² = | Center: (-1,-5) 17. x² + y² = 24x + 4y - 85 x²-24x + y²-4y = -85 = X²-24x + 144 + y²-4y +4 = -85 + 144 +4 (x-12)² + (y-2)² = 63 Standard Form: Diameter: 6 Diameter: 2 (x-12)²+(y-2)² = 63 14. x² + y²4x-12y-129 = 0 (49.9) (x-2)² + (Y-6)² = 169 Standard Form: (x-2)² + (y-6) ² = 169 Center: (2,6) Radius: 13 16. x² + y²-16x-161=0 x²-16x + y² = 161 x²-16x + 64 + y² = 161 +64 2 (x-8) ² + y² = 225 Standard Form: (X-8)² + y² = 225 Center: (8,0) Diameter: 30 18. x² + y²-9x+2y=x-6y +59 x²-10x + y² +8y=59 x²-10x+25+ y² +84 +16= 59+25+16 (x−5)² + (y + 4)² = 100 Standard Form: (x-5)² + (y+4)² = 100 Circumference: Radius: 10 Area: 100T (314.2) Ⓒ Gina Wilson (All Things Algebra, LLC), 2015-2019
Equation of a Circle
Standard form equation of a Circle
What is the standard form equaton of a circle?
Answer : is a way to express the definition of a circle on the coordinate plane.
The formula is $$(x -h)^2 + (y - k)^2 =r^2 $$ .
- h and k are the x and y coordinates of the center of the circle
- $$(x-9)^2 + (y-6)^2 =100 $$ is a circle centered at (9, 6) with a radius of 10
Another Example
Definition of Circle
--> Definition: A circle is the set of all points that are the same distance, r, from a fixed point. --> General Formula: X 2 + Y 2 =r 2 where r is the radius. --> parabolas , circles ALWAYS have X 2 and Y 2 terms. --> --> X 2 + Y 2 =4 is a circle with a radius of 2 (since 4 =2 2 ) --> locus of points. A circle is all of the points that are a fixed distance, known as the radius, from a given point, known as the center of the circle. --> here for a larger version) -->