Graph Circles in Expanded Form
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 2 questions completed
Questions:
- 1
- 2
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- Answered
- Review
-
Question 1 of 2
1. Question
Identify the centre and radius, then sketch the following circle.`2x^2+4x+2y^2-16y+18=0`Hint
Help VideoCorrect
Nice Job!
Incorrect
Help VideoIn 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^2-16y+18=0``x^2+2x``+``y^2-8y``+9=0`Now complete the squares.Start by adding constants to the expressions `x^2+2x` and `y^2-8y`.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^2-8y` 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 left-hand side, add `1``+``16``=17` to the right-hand side`x^2+2x+1``+``y^2-8x+16``+9=17`Now use the facts that `x^2+2x+1=(x+1)^2` and `y^2-8x+16=(y-4)^2` to rewrite these parts in the equation.`(x+1)^2``+``(y-4)^2``+9=17`Subtract `9` from both sides of the equation and finish rewriting in standard form.`(x+1)^2+(y-4)^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^2-4x+6y-3=0`Hint
Help VideoCorrect
Well Done!
Incorrect
Help VideoIn 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 left-hand side so the terms with the same variables are together.`x^2-4x``+``y^2+6y``-3=0`Now complete the squares.Start by adding constants to the expressions `x^2-4x` and `y^2+6y`.The constant to add to `x^2-4x` 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 left-hand side, add `4``+``9``=13` to the right-hand side`x^2-4x+4``+``y^2+6y+9``-3=13`Now use the facts that `x^2-4x+4=(x-2)^2` and `y^2+6x+9=(y+3)^2` to rewrite these parts in the equation.`(x-2)^2``+``(y+3)^2``-3=13`Add `3` to both sides of the equation and finish rewriting in standard form.`(x-2)^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