MAPLE(math program) Question2?

Question

How to do it by Maple?

The figure shows a circle with radius 1 imscribed in the parabola y=x^2 Fins the center of the circle.

help!!!
and thx for helping !

Answer 1

(0,5/4)

I solved this problem a few days ago using algebra.

You take the derivative of x^2, take the negative reciprocal (it will be -1/(2x) This will be the equation of the line you are looking for. The tangent points of the circle and parabola is perpendicular to the radius which goes through the center. You have two different formulae for the slope, and the fact that the radius is one (use distance formula). Then solve it and get the answer.



Sorry that's not by Maple, but it can be used to double-check your answer I guess. If you want me to work it out in full, add a note and I will.


Hopes this helps.

Answer 2

Graph y = x^2 for visualization
differentiate to get the tangent line y = 2x.
Generate the point -slope form y - b = 2(x - a)
generate the point-slope of the orthogonal at (a,b),
y - b = -(1/2)(x - a), and put it into slope-intercept form,
y = -(1/2)x + (a/2 + b), (a/2 + b) being the y-intercept of the radius af any inscribed tangent circircle
Now, (a - 0)^2 + (b - a/2 - b)^2 = 1
Solve for a,
a^2 + a^2/4 = 1
5a^2 = 4
a = 2/√5
b = 4/5
a/2 + b = √5/5 + 4/5 = (4 + √5)/5

Answer 3

homeless with a family contributors because i ought to get a job. also i ought to nicely be with my family contributors. if i have been wealthy i ought to experience trapped. money would not purchase each and every thing besides. you may nicely experience free in the experience that your wealthy, yet not chuffed that your on my own. so yea, homeless with a family contributors!