Circle Worksheet Day 1 Notes

Circles Worksheet Day #1 Write an equation of a circle given the following information. 1. Center (2, -4) Radius 4 Equation __________________________ 2. (-7, 1) 15 __________________________ 3. (3, 0) 1/3 __________________________ 4. (-5, -3) 3 2 __________________________ Write an equation of each circle described below. Show work! 5. Given a circle with center (3, -4) and passing through (6, 2). 6. Given a circle with the center (5, 1) and a point on the circle (8, -2). 7. Given a circle with the center at the origin and passing through (4, 3). Extension (Hint: find the coordinates of the center first) 8. Given a circle with (5, 1) and (3, -1) as the endpoints of the diameter. 9. Given a circle with (2, 1) and (6, -3) as the endpoints of the diameter. 10. Given a circle with (4, -3) and (2, 1) as the endpoints of the diameter. Circles – Notes Day 1 General Form of the Equation of a Circle:  )2 + ( Center: ( , ( )2 = ___2  ) and radius = ____ Given the center and radius, write the equation. 1. C (5, 2) ( r = 7 )2 + (  )2 = ___2  Equation: __________________________ 2. C (-3, 4) (  r = 2 5 )2 + ( )2 = ___2  Equation: __________________________ Given the center and another point on the circle, write the equation. To find r2 either plug in the point or use the distance formula, d  3. Find r2 by plugging in the point ( , ): C (4, -7) and (5, 3) (  )2 + ( ø x2  x1 ù2  ø y2  y1 ù2 . )2 = ___2  Equation: ______________________ 4. C origin and (-5, 2) (  )2 + (  Find r2 using the distance formula: )2 = ___2 Equation: ______________________ Circles Notes Day 2 Part 1: Rewriting equation in standard form If the quadratic equation isn’t in the standard form for a circle: ø x  hù 2  ø y  k ù 2  r 2 we must first complete the square to get it in the correct form. 1. x 2  y 2  16 x  22 y  20  0 Steps to complete the square. First, prepare the terms:  Group ____ and leave a space.  Group ____ and leave a space.  Move the constant and leave _____ _________. Then, complete the square:  ½ the linear term and square it.  Add to both sides.  Do this for both x and y.  Factor and simplify. 2. x 2  y 2  12 x  8 y  32  0 Part 2: Graphing Circles 2 1. øxù  ø yù C=( , 2  36 ) r = ______ 2. ø x  3 ù2  ø y  4 ù2  25 C=( , ) r = ______ 3. ø x  5 ù2  ø y  4 ù2  41 C=( , r = ______ ) Circles Worksheet Day #2 Put each equation in standard form and graph the circle. 1. x2 = 9 – y2 2. 2x2 + 2y2 – 8 = 0 3. x2 + y2 + 4y + 4 = 9 4. x2 + 6x + y2 = 7 5. y2 + x2 + 4x – 4y – 1 = 0 6. 5x2 + 20x + 5y2 = 35 7. 4x2 + 4y2 + 32y - 36 = 0 8. x2 + y2 – 3x + 8y = 20 9. x2 – 12x + 84 = -y2 + 16y 10. x2 + y2 + 2x + 4y = 11