Find the equation of a circle that has a diameter with the endpoints given by the points A(1,1) and B(2,4)

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

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

2 |

h = | 1 + 2 |

2 |

h = | 3 |

2 |

h = 1.5

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

2 |

k = | 1 + 4 |

2 |

k = | 5 |

2 |

k = 2.5

From above, the center of our circle is (h, k) = (1.5, 2.5)

r = Square Root((x

r = Square Root((2 - 1)

r = ½Square Root((1

r = ½√(1 + 9)

r = ½√10

r = ½√10

r = ½(3.4)

r = 1.5811

Find the equation of the circle with center (h,k) = (1.5,2.5) and radius r = 1.5811

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

(x - 1.5)

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: