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Jamaal converted the following conic equation from general form to standard form.


amaal converted the following conic equation from general form to standard form.

4x2 + 4y2 – 16x + 24y – 12 = 0

4x2 – 16x + 4y2 + 24y = 12

4(x2 – 4x) + 4(y2 + 6y) = 12

4(x2 – 4x + 4) + 4(y2 + 6y + 9) = 12 + 4 + 9

4(x – 2)2 + 4(y + 3)2 = 25

Jamaal identifies the center of the circle as

(2, –3) and the radius as r = Five-halves.

What error, if any, did Jamaal make ?

Jamaal misidentified the center. The center should be at the point (–2, 3).
Jamaal did not complete the square correctly; he should have added 16 and 36 inside the parentheses in step 4. The radius is r = StartRoot 55 EndRoot.
Jamaal added 4 and 9 to the right hand side in step 4; he should have added 16 and 36. The radius is r = 8.
Jamaal did not make an error.

Respuesta :

Answer: C. Jamaal added 4 and 9 to the right hand side in step 4; he should have added 16 and 36. The radius is r=8.

Step-by-step explanation: edge 2020, i took one for the team boys :(

In the given conic equation, Jamaal added 16 and 36 on the left hand side. However, he added 4 and 9 on the right hand side. The radius is r = 8.

What is a general conic equation?

Ax² + Bxy + Cy² + Dx + Ey + F = 0, where x, y are variables and A, B, C, D, E, F are constant terms.

Given,

4x² + 4y² – 16x + 24y – 12 = 0

⇒ 4x² – 16x + 4y² + 24y = 12

⇒ 4(x² – 4x) + 4(y² + 6y) = 12

⇒ 4(x² – 4x) + 16 + 4(y² + 6y) + 36 = 12 + 16 + 36

⇒ 4(x² – 4x + 4) + 4(y² + 6y + 9) = 12 + 16 + 36

⇒ 4(x – 2)² + 4(y + 3)² = 64

⇒ 4(x – 2)² + 4(y + 3)² = (8)²

Therefore, the center is at (2, -3) and the radius is r = 8.

Jamaal must have added 16 and 36 on the rest hand side of the conic equation. That's the mistake Jamaal did. As a result, the value of the radius is wrong when Jamaal solved.

Learn more about conic equation here: https://brainly.com/question/26909560

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