I have a little problem with a question:
What is the radius of a a circle that touches the parabola 1/2x² at (2,2) and the x-axis?
Here the derivative of our parabola is y=x
And if we get
This could give us the common point between those two circles; that would be the center of the circle that we want.
But this gives me a strange equation, that I really don't know what it is for.
Get the center (a,b)
and use it at the circle equation.
But where does (2,2) enters here?
I saw something about using both at the same equation, like:
Is this possible? Aren't x and y fixed values here?
Thanks! I can't find a good source to research on this.
Oh, sorry to not make myself clear, emakarov.
v is the x coordinate of the place where the circle touches the x-axis. The Xo in your graph.
I read somewhere that you could get get center of the circle by using two circles in the places where we have points, the parabola and the x-axis.
Using this formula I'll get a equation with some unwanted X's and Y's and V's, so it's probably not the best idea to use it.
I really thought about using a perpendicular here. But what is the easiest way to get it?
I would use it like f(x-2)+2 using the translation principles.
But what about the tangent line?
To get it you used right?
I was kind of confused in that terms too, since I hadn't seen calculus in some time.
Ok, I will give it a go one more time.
Thanks again, emakarov!
I've managed to do it!!!
Yes, it was quite easy with your explanation! Thank you so much!
There's another way that I don't understand well
What's that -1 and that 2?
I'm not sure, but the b^2-5b+5 could be acquired in some way, replacing a for b in the first equation.
This way it was answered in terms of y, it seems easier to use x though!