1
0
1
0
1
1
The line tangent to the curve
The line tangent to the curve
, and the equation is
The normal line at
at the origin is y = 0, or the x-axis. The normal line is x = 0, or the y-axis.
at the point
has slope
, and is
. The normal line has slope
.
intersects the y-axis (the normal line at the origin) at
. That is, the circle of best fit to the parabola
at the origin has center
. And
, and hence has radius
is
.
5
4
3
2
1
0
1
5
4
3
2
1
0
The line tangent to the curve
The line tangent to the curve
at the origin is
at the point
The normal line has slope
The normal line at
That is, when
1
. The normal line is
has slope
, and is
.
.
, and the equation is
intersects the line
(the normal line at
.
) when
.
. Now using L'Hospitals's rule, we see that
. And when x = -2, we have that y = -3 on the normal line y = -x + 1.
That is, the circle of best fit to the curve
at the point (0,1) has center
, and hence has radius
.