Equation of an ellipse and tangents

[Kartik.]

1) If we have the focus as (f,g) and the directrix as Ax+By+C =0 and the eccentricity as e we define the equation of the ellipse to be

(x-f)²+(y-g)² = e²(Ax+By+C)² / A²+B²

Does this imply that the variables x and y in the locus of the directrix and the ellipse refer to the same thing?(we do take them as similar or say like variables)

2) How can we find the points of intersection of the tangents(from a point outside the curve) on an elliptical curve?

 

[tiny-tim]

Hi Kartik!

1) If we have the focus as (f,g) and the directrix as Ax+By+C =0 and the eccentricity as e we define the equation of the ellipse to be

(x-f)²+(y-g)² = e²(Ax+By+C)² / A²+B²

Does this imply that the variables x and y in the locus of the directrix and the ellipse refer to the same thing?(we do take them as similar or say like variables)

No!

Ax+By+C = constant is a series of parallel lines that fill out the plane.

If the constant is zero, the line is the directrix, and (x,y,z) lies on the directrix.

If the constant isn't zero, that tells you how far away from the directrix the line (and (x,y,z) itself) is

2) How can we find the points of intersection of the tangents(from a point outside the curve) on an elliptical curve?

uhh?

isn't that just the original point? ​