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leva [86]
3 years ago
10

Consider a circle whose equation is x2 + y2 + 4x - 6y - 36 = 0. Which statements are true? Check all that appl"

Mathematics
1 answer:
Oduvanchick [21]3 years ago
8 0

Answer:

<h2>To complete the square for the x terms, add 4 to both sides.</h2>

To convert the given equation of the circle to standard form we should do as follows.

<h3>1. Add 36 to both sides of the equation.</h3>

x^{2} +y^{2}+4x-6y-36+36=36\\ x^{2} +y^{2}+4x-6y=36

<h3>2. We order the terms according to their variables.</h3>

x^{2} +4x +y^{2}-6y=36

<h3>3. Divide the linear term by 2, then elevate it to the square power.</h3>

x^{2} +4x + (\frac{4}{2} )^{2} +y^{2} -6y+(\frac{6}{2} )^{2} =36

<h3>4. Solve operations, and add the same units to the other side of the equation.</h3>

x^{2} +4x+4+y^{2} -6y+9=36+4+9\\

<h3>5. Now, we sum costant terms, and factor both trinomials.</h3>

(x+2)^{2} +(y-3)^{2} =49

As you can observe, the circle has center at (-2,3) and it has a radius of 7 units.

Notice that the second choice is correct, because we added 4 units to both sides to complete the square for the x terms.

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