The equation of x² + 6x + y² - 8y = 19 in standard form is (x + 3)² + ( y - 4)² = 44. Hence, Option A is the correct answer.
What is a system of equations?
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We have been given the equation as;
x² + 6x + y² - 8y = 19
We need to find the standard form of the equation.
Thus, we have,
(x² + 6x )+(y²- 8y) = 19
We shall complete the square for the term;
(x² + 6x + 9 - 9 ) + (y² + 4y + 16 - 16) = 19
Simplifying, we get,
(x² + 6x + 9) - 9 + (y²- 8y + 16) - 16 = 19
(x² + 6x + 9) - 9 + (y²- 8y + 16) - 16 = 19 + 9 + 16
Formula used :
x²+2xy+y² = (x+y)²
x²-2xy+y² = (x-y)²
Simplifying, we get,
(x + 3)² + ( y - 4)² = 44
Thus, the equation of x² + 6x + y² - 8y = 19 in standard form is (x + 3)² + ( y - 4)² = 44.
Hence, Option A is the correct answer.
Learn more about equations here;
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