What is the correct standard form of the equation
√(x−2)2+(y+4)2
explain each step
To find the correct standard form of the equation, we need to simplify the expression inside the square root and expand it.
Step 1: Distribute the square to both terms inside the parentheses:
= √(x^2 - 4x + 4 + y^2 + 8y + 16)
Step 2: Combine like terms:
= √(x^2 + y^2 - 4x + 8y + 20)
So, the correct standard form of the equation is √(x^2 + y^2 - 4x + 8y + 20).
To find the correct standard form of the equation √(x−2)2+(y+4)2, we need to simplify and rewrite the equation in a standard form that is separated by individual terms for x and y.
Step 1: Simplify the equation
√(x−2)2+(y+4)2 = (x−2)+(y+4)2
Step 2: Expand the square of (y+4)
(x−2)+(y+4)2 = (x−2)+(y+4)(y+4)
= x−2+(y2+4y+4y+16)
= x−2+(y2+8y+16)
= x−2+y2+8y+16
Step 3: Rearrange the terms
x−2+y2+8y+16 = x+y2+8y−2+16
= x+y2+8y+14
Therefore, the correct standard form of the equation √(x−2)2+(y+4)2 is x+y2+8y+14.