anonymous
  • anonymous
A circle has the same center point as an ellipse whose equation is 32x^2+18y^2-128x-180y+290=0.If the circle just fits inside ellipse,what is the diameter of the circle?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Keep in mind a circle is really just an ellipse with major and minor axes being the same length. An ellipse is really just a stretched out circle in one direction, so we want to find the length of the minor axis of the ellipse and that will be our diameter. A bit of rearranging... 32x^2 - 128x + 18y^2 - 180y = -290 16x^2 - 64x + 9y^2 - 90y = -145 16(x^2 - 4x + ______) + 9(y^2 - 10y + ______) = -145 + ______ + ______ Complete the square: 16(x^2 - 4x + 4) + 9(y^2 - 10y + 25) = -145 + 64 + 225 16(x - 2)^2 + 9(y - 5)^2 = 144 \[(x - 2)^2/9+(y -5)^2/16 = 1\] From our ellipse equation, we can see that our a^2 = 9 --> a = 3. Now, this is only one half of the minor axis, so we only have the radius of the circle. The diameter is 2*3 = 6.

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