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3 years ago

The equation of a circle in general form is x2+y2+20x+12y+15=0 . What is the equation of the circle in standard form?

Mathematics

2 answers:

mestny [16]3 years ago

6 0

Answer:

(x)²+(y)²=0

Step-by-step explanation:

Mariulka [41]3 years ago

4 0

<u>ANSWER</u>

${(x + 10)}^{2} + {(y + 6)}^{2} = 121$

<u>EXPLANATION</u>

The equation of the circle in general form is given as:

${x}^{2} + {y}^{2} + 20x + 12y + 15 = 0$

To obtain the standard form, we need to complete the squares.

We rearrange the terms to obtain:

${x}^{2} + 20x + {y}^{2} + 12y = - 15$

Add the square of half the coefficient of the linear terms to both sides to get:

${x}^{2} + 20x +100 + {y}^{2} + 12y + 36 = - 15 + 100 + 36$

Factor the perfect square trinomial and simplify the RHS.

${(x + 10)}^{2} + {(y + 6)}^{2} = 121$

This is the equation of the circle in standard form.

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There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:

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$b = \frac{\left|\begin{array}{ccc}r_{1}^{2}&0&1\\r_{2}^{2}&0&1\\x^{2}&y&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }$

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The equation of a circle in general form is ​ x2+y2+20x+12y+15=0 ​ . What is the equation of the circle in standard form?

The equation of a circle in general form is x2+y2+20x+12y+15=0 . What is the equation of the circle in standard form?