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.

$(x+2)^2+(y-4)^2=25$
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In order to graph the circle, first find the centre and radius

The 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
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.
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In order to graph the circle, first find the radius

The 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

Graph Circles in Standard Form

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1. Question

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Fantastic!

2. Question

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Excellent!

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