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Ch. 10 Day 1

CIRCLES. Ch. 10 Day 1. Ch. 10: We will study: Conic Sections When a plane intersects a right circular cone, the result is a conic section. The four types are:. Circle. Standard Equation if center is the origin. Standard Equation if ( h,k ) is the center. x 2 +y 2 = r 2.

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Ch. 10 Day 1

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  1. CIRCLES Ch. 10 Day 1

  2. Ch. 10: We will study: Conic Sections When a plane intersects a right circular cone, the result is a conic section. The four types are:

  3. Circle Standard Equation if center is the origin Standard Equation if (h,k) is the center x2 +y2 = r2 (x-h)2 +(y-k)2 = r2 r = radius

  4. (x-h)2 +(y-k)2 = r2 Circle Find the equation of a circle that has a center =(2,-1) and a radius equal to 3 (x-h)2 +(y-k)2 = r2 (x-2)2 +(y- -1)2 = 32 (x-2)2 +(y+1)2 = 9

  5. Circle (x-h)2 +(y-k)2 = r2 Find the equation of a circle that has a center = (0,3) and a point on the circumference of the circle is (-4,6) (x)2 +(y-3)2 = 52 (x)2 +(y-3)2 = 25 (3)2 +(4)2 = r2 r = 5 First find the radius!

  6. Circle (x-h)2 +(y-k)2 = r2 Find the equation of a circle that has (2,-3) and (-10,-8) as the endpoints of a diameter. (x+4)2 +(y+5.5)2=(6.5)2 Center: (-4,-5.5) d =13 so r = 6.5 (5)2 +(12)2 = d2 Now find the radius (x+4)2 +(y+5.5)2=42.25 First find the center!

  7. Change the equation from non-standard form to standard form (x-h)2 +(y-k)2 = r2

  8. Write the equation in standard form (x-h)2 +(y-k)2 = r2

  9. (x-h)2 +(y-k)2 = r2 Circle Find the equation of a circle, in standard form, that has a center =(-2,-6) and is tangent to the line x=3 (x-h)2 +(y-k)2 = r2 (x+2)2 +(y+6)2 = 52 (x+2)2 +(y+6)2 = 25

  10. (x-h)2 +(y-k)2 = r2 Circle Find the equation of a circle, in standard form, that has a center in quadrant 1 and is tangent to the lines x=-3, x=5, and the x-axis (x-h)2 +(y-k)2 = r2 (x-1)2 +(y-4)2 = 42 (x-1)2 +(y-4)2 = 16 Center: (1,4) Domain: Range: Circumference: Area:

  11. HW Practice 10.1 is optional • hints: • #3 Divide by 3 first • #4 Add 8 first • Remember the right side of the equation is r2…not r • Simplify radicals if you can but do not convert them to decimals!

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