Question 851968
How to find the equation of the conic with center at (-4,1), one focus at (-1,1) and corresponding directrix at x=13/4?
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This conic is an ellipse with horizontal major axis with center at (-4,1)
Its standard form of equation: {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}, a>b, (h,k)=center
c=3 (distance from center to foci on the major axis)
directrix at {{{x=13/4=a/e=a/(c/a)=a^2/c}}}
a^2=13c/4=39/4
b^2=a^2-c^2=39/4-9=39/4-36/4=3/4
equation:
 {{{(x+4)^2/(39/4)+(y-1)^2/(3/4)=1}}}