Obtain the equation of the conic, a focus of which lies at (2,1), the directrix of which is x+y = 0 and which passes through (1,4). Also identify the conic.
Answer:-
The distance of point (1,4) from focus at (2,1) is
The distance of point(1,4) from directrix is
and ratio of distances is
As the ratio is less than 1, it is an ellipse
and the equation is obtained from ratio of the distance of a point on ellipse say (x,y) from focus (2,1) and its distance from directrix
x+y=0 being . the latter is , hence equation is
=
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