Discover MakerZone

MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi test

Learn more

Discover what MATLAB® can do for your career.

Opportunities for recent engineering grads.

Apply Today

MATLAB Academy

New to MATLAB?

Learn MATLAB today!

Problem 282. Circle and Quadratic

Created by Matt Fig

Imagine the quadratic curve with equation


On the concave side of this curve there is a circle of radius R. The circle is as close the the extremum of the quadratic as possible without resulting in the curves crossing each other. Write a function which takes as inputs a,b,c, and R and returns the coordinates of the center of the circle.

For example, if

a=1; b=0; c=10; R=pi; 

then the function returns

T = circ_puzz(a,b,c,R)
T =
     0   20.1196044010894

This can be visualized as follows:

 P = @(x) a*x.^2 + b*x + c;  % Quadratic
 C = @(x) real(-sqrt(R^2-(x-T(1)).^2) + T(2));  % Lower half circle
 x = linspace(-R,R,10000);  % Range of plotted data.
 axis equal


Problem Group

Solution Statistics

25 correct solutions 46 incorrect solutions
Last solution submitted on May 13, 2015

Problem Comments

Solution Comments