Question

Write the equation x² + 6x + y² – 8y = 19 in standard form.

Question 17 options:


1)


(x – 3)²+ (y – 4)² = √44


2)


(x + 3)² + (y + 4)² = 44


3)


(x + 3)² + (y – 4)²= 44


4)


(x + 3)² + (y – 4)² =√44

Answer 1

Formula used :

• x²+2xy+y² = (x+y)²
• x²-2xy+y² = (x-y)²

`→{x}^(2) + 6x + {y}^(2) - 8y = 19 \\ ({x}^(2) + 2.3.x + {3}^(2) ) +({y}^(2) - 2.4.y + {4}^(2) ) = 19 + {3}^(2) + {4}^(2) \\ {(x + 3)}^(2) + {(y - 4)}^(2) = 19 + 9 + 16 \\ \boxed{ {(x + 3)}^(2) + {(y - 4)}^(2) = 44}✓`

• 3) (x+3)²+(y-4)²=44 is the right answer.

Answer 2

option C

Explanation:

using (X + 3)² + ( y - 4)² = 44

gives you directly x² + 6x + y² - 8y = 19