A line tangent to a circle $x^2 + y^2 = r^2$ at $x=2$

Question

The question stated that the line has a positive gradient, tangent to the line at $x=2$,

Is it even possible? Since if the line tangent at $x=2$ means it has negative gradient.

Let's make another circle perpendicular to the previous line, that line is y2=x, it has a positive gradient, makes the line tangent to the circle y1 has a negative gradient.

It is impossible for y2 to have negative gradient, because it must goes to (0,0)(2,2) to be perpendicular to y1..

Where was i wrong?

Answer 1

You want a line with positive gradient which touches the circle at $x=2$. That means the circle must have a point $(2,y)$ which means that $r\ge2$. So assume that is true. Draw a picture.

Can you finish? What happens if $r=2$?