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Mathematical calculation skills of directrix or asymptote
You may be confused.

The ellipse has no asymptote, so the directrix can be written directly by the formula X = A 2/c or Y = A 2/C. ..

Hyperbolic directrix equation is exactly the same as ellipse. Asymptote equation can regard 1 in the formula as 0 and expand it with square difference.

For example: x 2-y 2 = 1, rewritten as x 2-y 2 = 0, that is,

(x+y)(x-y)=0,∴y= X. The focus can be on the X axis or the Y axis.