Find the equation of a circle that has a diameter with the endpoints given by the points A(1,4) and B(5,6)

Step 1: Find the Midpoint (h,k) of AB:

h = | A_{1} + B_{1} |

2 |

h = | 1 + 5 |

2 |

h = | 6 |

2 |

h = 3

k = | A_{2} + B_{2} |

2 |

k = | 4 + 6 |

2 |

k = | 10 |

2 |

k = 5

From above, the center of our circle is (h, k) = (3, 5)

r = Square Root((x

r = Square Root((5 - 1)

r = ½Square Root((4

r = ½√(16 + 4)

r = ½√20

r = ½√20

r = ½(4.6)

r = 2.2361

Find the equation of the circle with center (h,k) = (3,5) and radius r = 2.2361

The standard equation for a circle is (x - h)

(x - 3)

Expanding the standard form, we get the general form of x

Expanding the standard form, we get the general form of x

x

Combining our constants, we have our general form of a circle equation below: