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Question

The length of the latus-rectum of the conic 3x2+4y26x+8y5=0 is unit.

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Solution

3x2+4y26x+8y5=0
3(x22x)+4(y2+2y)=5
3(x22x+1)+4(y2+2y+1)=5+3+4
3(x1)2+4(y+1)2=12
(x1)24+(y+1)23=1
So, a=2 and b=3(a>b).

Latus rectum =2b2a
=2×32
=3 unit

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