Mathematics

Mathematics

Problem

The equations of the transverse and conjugate axes of a hyperbola are x+2y−3=0x + 2y - 3 = 0 and 2x−y+4=02x - y + 4 = 0 respectively and their respective lengths are 2\sqrt{2} and 23\frac{2}{\sqrt{3}} . The equation of the hyperbola is a. 2(x+2y−3)2−3(2x−y+4)2=52(x + 2y - 3)^2 - 3(2x - y + 4)^2 = 5 b. 2(2x−y+4)2−3(x+2y−3)2=52(2x - y + 4)^2 - 3(x + 2y - 3)^2 = 5 c. 2(x+2y−3)2−3(2x−y+4)2=12(x + 2y - 3)^2 - 3(2x - y + 4)^2 = 1 d. 2(2x−y+4)2−3(x+2y−3)2=12(2x - y + 4)^2 - 3(x + 2y - 3)^2 = 1

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