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Ellipse Problem

Source: 1988 National High School Mathematics League, Exam One, Problem 2

February 25, 2020
conicsellipse

Problem Statement

If the coordinate origin is inside the ellipse k2x2+y2−4kx+2ky+k2−1=0k^2x^2+y^2-4kx+2ky+k^2-1=0, then the range value of kk is (A)∣k∣>1(B)∣k∣≠1(C)−1<k<1(D)0<∣k∣<1\text{(A)}|k|>1\qquad\text{(B)}|k|\neq1\qquad\text{(C)}-1<k<1\qquad\text{(D)}0<|k|<1
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