Question 299715
what are the possible coordinates of a point where the line y=x-4 and the circle x^2+y^2=40 meet. thank you !!!!!
<pre><font size = 4 color = "indigo"><b>
{{{drawing(300,300,-10,10,-10,10, 
locate(6,2,"(6,2)"), locate(-5,-6,"(-2,-6)"),
graph(300,300,-10,10,-10,10,x-4), red(circle(0,0,sqrt(40))) )}}} 

Here's how to find those points algebraically:

{{{system(y=x-4,x^2+y^2=40)}}}

Substitute {{{(x-4)}}} for y in the second equation:

{{{x^2+y^2=40}}}
{{{x^2+(x-4)^2=40}}}
{{{x^2+(x-4)(x-4)=40}}}
{{{x^2+x^2-4x-4x+16=40}}}
{{{2x^2-8x+16=40}}}
{{{2x^2-8x-24=0}}}
{{{x^2-4x-12=0}}}
{{{(x-6)(x+2)=0}}}
{{{matrix(2,2,
"x-6=0","x+2=0",
"x=6",    "x=-2")}}}

Substitute 6 for x in {{{y=x-4}}}

{{{y=x-4}}}
{{{y=6-4}}}
{{{y=2}}}

So one point is (x,y) = (6,2)

Substitute -2 for x in {{{y=x-4}}}

{{{y=x-4}}}
{{{y=-2-4}}}
{{{y=-6}}}

So the other point is (x,y) = (-2,-6)

Edwin</pre>