Question 189634
Equation of a Circle
7. The point (a, 8) lies on the circle defined by x^2+y^2=100.
a) Explain why there are two possible values for a.
Find these values. 
<pre><font size = 4 color = "indigo"><b>
Here is why there are two possible values:

When you substitute x=a and y=8 into

{{{x^2+y^2=100}}}

you get

{{{a^2+8^2=100}}}

Then you simplify and solve for {{{a^2}}}.

{{{a^2+64=100}}}
{{{a^2=100-64}}}
{{{a^2=36}}}

But then when you take the square root, there
are two square roots of 36, and so you get:

{{{a=" "+-sqrt(36)}}}

which means these two answer:

{{{a=6}}} and {{{a = -6}}}

</pre></font></b>
b) Use a graph to check that the points corresponding to both values for a are on the circle.
<pre><font size = 4 color = "indigo"><b>
{{{drawing(400,400,-11,11,-11,11,line(-6.3,8,-5.7,8), line(-6,7.7,-6,8.3),
line(6.3,8,5.7,8), line(6,7.7,6,8.3), locate(6,8,"(6,8)"), locate(-6,8,"(-6,8)"),
graph(400,400,-11,11,-11,11), circle(0,0,10) )}}}

You can see that both points (-6,8) and (6,8) are on
the circle {{{x^2+y^2=100}}}
Edwin</pre>