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Rectangular Coordinate System

Source: 1997 National High School Mathematics League, Exam One, Problem 4

March 4, 2020
conicsellipse

Problem Statement

In rectangular coordinate system, if m(x2+y2+2y+1)=(x−2y+3)2m(x^2+y^2+2y+1)=(x-2y+3)^2 refers to an ellipse, then the range value of mm is (A)(0,1)(B)(1,+∞)(C)(0,5)(D)(5,+∞)\text{(A)}(0,1)\qquad\text{(B)}(1,+\infty)\qquad\text{(C)}(0,5)\qquad\text{(D)}(5,+\infty)
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