/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 86 Find the equation of the circle ... [FREE SOLUTION] | 91影视

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Chapter 8: Problem 86

Find the equation of the circle $$x^{2}+y^{2}+D x+E y+F=0$$ that passes through the points. To verify your result, use a graphing utility to plot the points and graph the circle. $$(0,0),(0,6),(3,3)$$

Short Answer

Expert verified
The equation of the circle is \(x^{2}+y^{2}-3x-6y+0=0\)

Step by step solution

01

Substitute the given points into the equation

Substitute each of the points (0,0), (0,6), (3,3) into the equation \(x^{2}+y^{2}+D x+E y+F=0\). This will give the following three equations: Substituting (0,0) yields: \(0^{2} + 0^{2} + D(0) + E(0) + F = 0\) which simplifies to \(F = 0\)Substituting (0,6) yields: \(0^{2} + 6^{2} + D(0) + E(6) + F = 0\) which simplifies to \(E = -6\)Substituting (3,3) yields: \(3^{2} + 3^{2}+ D(3) + E(3) + F = 0\) which simplifies to \(D = -3\)
02

Combine the results

Combine the results of the substitutions to form the equation of the circle. Using the coefficients D, E, F that were found, the equation is \(x^{2}+y^{2}-3x-6y+0=0\)
03

Verification

To verify the solution, graph the equation \(x^{2}+y^{2}-3x-6y+0=0\) using a graphing utility or software. The circle should pass through the points (0,0), (0,6), (3,3).

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