can you help me solve this:
In a system of axes consider the points A(-1,0) B(2,0) and M(x,y)
such that x²-x-2+y²=0
Here are those points plotted:
how can i find M ??
x² - x - 2 + y² = 0
x² - x + y² = 2
x² - x + + y² = 2 +
(x - )² + (y - 0)² =
So this is a circle with center (h,k) = (, 0) and r = =
We draw that circle:
M(x,y) is any point on that green circle, including the two given points.
There are an infinite number of solutions because there are an infinite
number of points on the circle.
Here are 4 possible solutions for M(x,y)
M(0,)
M(0,-)
M(1,)
M(1,-)
They are all on the circle. I'll plot them in red:
But realize that there are infinitely many solutions for M(x,y) since there
are infinitely many points on the green circle besides those 4 plotted
in red above.
Edwin