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Mariah converted the following equation into standard form.

25x2 + 25y2 – 200x + 100y + 4 = 0
25x2 – 200x + 25y2 + 100y = –4
25(x2 – 8x) + 25(y2 + 4y) = –4
25(x2 – 8x + 16) + 25(y2 + 4y + 4) = –4 + 16 + 4
25(x – 4)2 + 25(y + 2)2 = 16


She identified the conic as a circle with a center (4, –2) and a radius r = 4. What error, if any, did Mariah make?

Mariah did not make an error.
Mariah listed the center incorrectly. The center should be (–4, 2).
Mariah should have added 400 and 100 to the right side of the equation in step 4
Mariah factored incorrectly in step 5. She should have factored to (x – 8)2 and (y + 4)2.

Respuesta :

Answer:

C. Mariah should have added 400 and 100 to the right side of the equation in step 4

Step-by-step explanation:

I got it right on the QUIZ EDG21

      Option (3). Mariah should have added 400 and 100 to the right side of the equation in step 4.

Standard equation of a circle:

  • Standard equation of a circle is given by,

        (x - a)² + (y - b)² = r²

        Here, (a, b) is the center of the circle

        And r = radius of the circle

Equation given in the question → 25x² + 25y² - 200x + 100y + 4 = 0

Conversion of the equation into standard form,

25x² + 25y² - 200x + 100y + 4 = 0

25x² - 200x + 25y² + 100y = -4

25(x² - 8) + 25(y² + 4y) = -4

25(x² - 8x + 16) + 25(y² + 4y + 4) = -4 + 400 + 100

25(x - 4)² + 25(y + 2)² = 496

(x - 4)² + (y + 2)² = [tex]\frac{496}{25}[/tex]

     Hence, Mariah made an error in 4th step by adding 16 and 4 instead of adding 400 and 100 to the right side. Option (3) will be the correct option.

Learn more about the standard equation of a circle here,

https://brainly.com/question/24151497?referrer=searchResults

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