Question

半徑為5的圓過(guò)點(diǎn)A(－2,6),且以M(5,4)為中點(diǎn)的弦長(zhǎng)為2,求此圓的方程.

Answer 1

解:設(shè)圓心為P(a,b),則圓的方程為(x－a)²＋(y－b)²=25.

∵(－2,6)在圓上,∴(a＋2)²＋(b－6)²=25.                                                                    ①

又以M(5,4)為中點(diǎn)的弦長(zhǎng)為2,

∴|PM|²=5²－5,即(a－5)²＋(b－4)²=20.                                                                      ②

①－②得b=,代入①并解得a=1或a=,相應(yīng)的求得b=2或b=.

∴圓的方程為(x－1)²＋(y－2)²=25或(x－)²＋(y－)²=25.