5.4k views
5 votes
Write the equation x2 + 2x +y2 - 6y = 35 in standard form.

User Tamanakid
by
7.7k points

1 Answer

4 votes

Given


x^2+2x+y^2-6y=35

Complete the square for x, as shown below


\begin{gathered} x^2+2x+b=(x+a)(x+a)=x^2+2ax+a^2 \\ \Rightarrow2=2a\Rightarrow a=1 \\ \Rightarrow b=a^2=1 \end{gathered}

Therefore,


\begin{gathered} x^2+2x+1+y^2-6y=35+1=36 \\ \Rightarrow(x+1)^2+y^2-6y=36 \end{gathered}

Completing the square for y,


\begin{gathered} y^2-6y+b=(x+a)^2=x^2+2ax+a^2 \\ \Rightarrow-6=2a\Rightarrow a=-3 \\ \Rightarrow b=a^2=9 \end{gathered}

Then,


(x+1)^2+(y-3)^2=45

The answer is (x+1)^2+(y-3)^2=45. A circumference in its standard form.

User Maggie
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories