Geometry: An Interactive Journey to Mastery

 6KHLODFODLPVWKDWWKHWZRFLUFOHVJLYHQE\ͼ௘x௘ͽ^2 ͼ௘yí௘ͽ^2 = 49 and x^2 + y^2 – 6x + 16y + 37 = 0 are
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D௘ͽ /HWA ͼ௘௘ͽDQGB ͼ௘௘ͽ)LQGWKHHTXDWLRQRIWKHFLUFOHZLWKAB as its diameter.
E௘ͽ 6KRZWKDW\RXUDQVZHUWRSDUWD௘ͽFDQEHUHZULWWHQDVͼ௘xí௘ͽͼ௘xí௘ͽ^ ͼ௘yí௘ͽͼ௘yí௘ͽ 
F௘ͽ 6KRZWKDWLIA ͼ௘a 1 , a 2 ௘ͽDQGB ͼ௘b 1 , b 2 ௘ͽWKHQͼ௘xía 1 ௘ͽͼ௘xíb 1 ௘ͽ^ ͼ௘yía 2 ௘ͽͼ௘yíb 2 ௘ͽ LVLQGHHGWKH
equation of the circle with ABDVWKHGLDPHWHUͼ௘DOEHLWZULWWHQLQDGLIIHUHQWJXLVH௘ͽ