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?

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

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.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Not the answer you are looking for?

Search for more explanations.

Ask your own question