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Question

The equation of a conic section whose focus is at (1,0), directrix is the line 4x3y+2=0 and eccentricity is 12, is

A
34x2+24xy+41y2+84x+12y+46=0
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B
41x2+24xy+34y2+84x+12y+46=0
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C
34x2+24xy+41y2+12x+84y+46=0
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D
34x2+24xy+41y2+84x+12y+81=0
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Solution

The correct option is A 34x2+24xy+41y2+84x+12y+46=0
e=12 4x3y+2=0 directrix focus =(1,0)
f=(x+1)2+(y0)2
distance from (x,y) to the line 4x3y+2=0
d=4x3y+225=4x3y+25
e=fd12=5(x+1)2+(y0)2(4x3y+2)2
12=5(x2+2x+1+y2)(4x3y)2+4+16×12y
16x2+9y214xy+4+16x12y=50x2+100x+50+50
34x2+41y2+24xy+34x+12y+46=0

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