Answer:
(X+1)²+4(y+3)² = (√-20)²
Step-by-step explanation:
The standard form of expressing equation ic;
(x-a)²+(y-b)² = r²
Given the expression
x²+4y²+2x+24y+21 = 0
Collect the like terms
x²+2x + 4y²+24y+21 = 0
Completing the squares
x²+2x +(2/2)² + 4(y²+6y)+21 = 0+(2/2)²
x²+2x +(2/2)² + 4(y²+6y+(6/2)²)+21 = 0+(2/2)²
x²+2x +1 + 4(y²+6y+(3)²)+21 = 0+1
x²+2x +1 + 4(y²+6y+9)+21 = 0+1
x²+2x +1 + 4y²+24y+36+21 = 0+1
x²+2x +1 + 4(y²+6y+9)+21 = 0+1
x²+2x +1 + 4(y+3)²+21 = 0+1
(X+1)²+4(y+3)² = 1 - 21
(X+1)²+4(y+3)² = -20
(X+1)²+4(y+3)² = (√-20)²
