Problem 1121

Write the equation in standard form.

x2 + y2 + 4y – 45 = 0

 

Solution:-

 

Complete the square and then write the equation in standard form.

(x – h)2 + (y – k)2 = r2

Regroup the terms.

(x2) + (y2 + 4y) – 45 = 0

Since x is  square, there is nothing needed.

Now complete the square for y2 + 4y.

To complete the square, add and subtract 4 inside the second set of parentheses.

x2 + (y2 + 4y + 4 – 4 ) – 45 = 0

Now remove the subtract term from within the parentheses.

x2 + (y2 + 4y + 4 – 4 ) – 45 = 0

Use the addition principle to get the constant terms on the right side of the equation.

x2 + (y2 + 4y + 4  ) = 49

Now writ the equation in standard form.

(x -h)2 + (y – k)2 = r2

(x – 0)2 + (y + 2)2 = 49

 

 

 

 

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