Imagine we drew a line from the centre (2,0) to the point (0,4).
Essentially the line we drew from the centre to that point on the circle is perpendicular to the tangent line slope-wise.
The slope of that line from the centre to the point is -2 based on the slope's equation or formula.
slope = [tex]\frac{y2-y1}{x2-x1}=\frac{4-0}{0-2} =-2[/tex]
Therefore the tangent equation's slope is 1/2 since any perpendicular line's slope is the negative reciprocal of the original line's slope.
By using the point-slope form, we must have the point on the tangent plane (0,4) and the slope we found which is 1/2.
[tex]y - 4 = \frac{1}{2}(x-0)\\ y= \frac{1}{2}x + 4[/tex]
Hope that helps!
