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Graph Circles in Expanded FormGraph Circles in Expanded Form
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Question 1 of 2
1. Question
Identify the centre and radius, then sketch the following circle.`2x^2+4x+2y^216y+18=0`Hint
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In order to graph the circle, first find the centre and radiusThe centre and radius can be read from the standard form equation`(x``h``)^2+(y``k``)^2=``r^2`where the centre is `(``h``,``k``)` and the radius is `r`Rewrite the given equation in standard form.Start by dividing both sides of the equation by 2.`2x^2+4x+2y^216y+18=0``x^2+2x``+``y^28y``+9=0`Now complete the squares.Start by adding constants to the expressions `x^2+2x` and `y^28y`.The constant to add to `x^2+2x` is half the coefficient of `x` squared.`(\frac{1}{2}\times2)^2=1^2=``1`The constant to add to `y^28y` is half the coefficient of `y` squared.`(\frac{1}{2}\times(8))^2=4^2=``16`Since you are adding `1` and `16` to the lefthand side, add `1``+``16``=17` to the righthand side`x^2+2x+1``+``y^28x+16``+9=17`Now use the facts that `x^2+2x+1=(x+1)^2` and `y^28x+16=(y4)^2` to rewrite these parts in the equation.`(x+1)^2``+``(y4)^2``+9=17`Subtract `9` from both sides of the equation and finish rewriting in standard form.`(x+1)^2+(y4)^2=8``(x``(1)``)^2+(y``4``)^2=``\sqrt{8}^2`In this equation `h=1``,``k=4` and `r=\sqrt{8}`The centre is `(``1``,``4``)` and the radius is `\sqrt{8}\approx 2.828`To sketch the circle first plot the centre `(``1``,``4``)`.Since the radius is `2.828`, plot the points which are `2.828` units above, below, left and right of the centre.Complete the sketch 
Question 2 of 2
2. Question
Identify the centre and radius, then sketch the following circle.`x^2+y^24x+6y3=0`Hint
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In order to graph the circle, first find the centre and radiusThe centre and radius can be read from the standard form equation`(x``h``)^2+(y``k``)^2=``r^2`where the centre is `(``h``,``k``)` and the radius is `r`Rewrite the lefthand side so the terms with the same variables are together.`x^24x``+``y^2+6y``3=0`Now complete the squares.Start by adding constants to the expressions `x^24x` and `y^2+6y`.The constant to add to `x^24x` is half the coefficient of `x` squared.`(\frac{1}{2}\times (4))^2=2^2=``4`The constant to add to `y^2+6y` is half the coefficient of `y` squared.`(\frac{1}{2}\times 6)^2=3^2=``9`Since you are adding `4` and `9` to the lefthand side, add `4``+``9``=13` to the righthand side`x^24x+4``+``y^2+6y+9``3=13`Now use the facts that `x^24x+4=(x2)^2` and `y^2+6x+9=(y+3)^2` to rewrite these parts in the equation.`(x2)^2``+``(y+3)^2``3=13`Add `3` to both sides of the equation and finish rewriting in standard form.`(x2)^2+(y+3)^2=16``(x``2``)^2+(y``(3)``)^2=``4^2`In this equation `h=2``,``k=3` and `r=4`The centre is `(``2``,``3``)` and the radius is `4`.To sketch the circle first plot the centre `(``2``,``3``)`.Since the radius is `4`, plot the points which are `4` units above, below, left and right of the centre.Complete the sketch
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