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Question

Write the centre and eccentricity of the ellipse 3x2 + 4y2 − 6x + 8y − 5 = 0.

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Solution

3x2-6x+4y2+8y-5=03(x2-2x)+4(y2+2y)=53(x2-2x+1)+4(y2+2y+1)=5+3+43(x-1)2+4(y+1)2=123(x-1)212+4(y+1)212=1(x-1)24+(y+1)23=1Compairing it withx2a2+y2b2=1, we get:a=2 and b=3Here, a>b, so the major and the minor axes of the ellipse are along the x-axis and y-axis, respectively.Now, e=1-b2a2e=1-34e=14 e=12 and centre = 1,-1

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