Graph Circles in Standard Form
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Question 1 of 2
1. Question
Identify the centre and radius, then sketch the following circle.`(x+2)^2+(y-4)^2=25`Hint
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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`(x-``(-2)``)^2+(y-``4``)^2=``5^2`In this equation `h=-2``,``k=4` and `r=5`The centre is `(``-2``,``4``)` and the radius is `5`To sketch the circle first plot the centre `(``-2``,``4``)`.Since the radius is `5`, plot the points which are `5` units above, below, left and right of the centre.
Complete the sketch
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Question 2 of 2
2. Question
Find the radius of the circle which has centre `(-1,-5)` and passes through `(2,-1)`. Then sketch this circle.Hint
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Help VideoIn order to graph the circle, first find the 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`.The centre of our circle is `(``-1``,``-5``)`, so in the standard equation `h=-1`` and ``k=-5``(x-``(-1)``)^2+(y-``-5``)^2=``r^2``(x+1)^2+(y+5)^2=``r^2`We know the point `(``2``,``-1``)`, lies on the circle, so we can substitute `x=2` and `y=-1` into the equation and solve to find `r`.`(``2``+1)^2+(``-1``+5)^2=``r^2``(3)^2+(4)^2=``r^2``9+16=``r^2``25=``r^2``r=5`To sketch the circle first plot the centre `(``-1``,``-5``)`.Since the radius is `5`, plot the points which are `5` units above, below, left and right of the centre.
Complete the sketch