The equation of the ellipse with directrix 3x+4y-5=0, focus (1 ,2 ) and eccentricity 12, is

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Accepted Answer

Correct answer: B. (b) The equation of ellipse with directrix 3x+4y-5=0, focus (1 ,2 ) and eccentricity 12. From basic definition We have (x- )^2+ (y- )^2=e Ax+ By+C A^2+B^2 Hence (x-1 )^2+ (y-2 )^2= 12 (3x+4y-5 )5 ⇒100(x^2+y^2-2x-4y+5)= (3x+4y-5 )^2 ⇒100(x^2+y^2-2x-4y+5)=9x^2+16y^2+25+24 xy ⇒-30x-40y ⇒91x^2+84y^2-24 xy-170x-360y+475=0

$The equation of the ellipse with directrix 3 x + 4 y - 5 = 0, focus (1, 2) and eccentricity \frac{1}{2}, is$

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