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Find the focus, directrix and vertex of the parabola x = .
Are the answers:
Focus ( , 3) OR (-5, 3)
Directrix x = - 6 OR x = - 7
Vertex (-6, 3)
If the answers are the former, could someone please show me how to do this question?
your answers are correct...
the given equation is x=y^2-6y+3
it can be written as
now shift the coordinate system such that x+6=X and y-3=Y
then the equation becomes Y^2=X
compare it with Y^2=4aX
we get a=1/4
Vertex X=o,Y=o but in new coordinate system i.e. XY system
or x+6=0 ,y-3=0 in orig. coordinate system i.e. xy system
Focus=(1/4,0) but in new coordinate system i.e.XY system
or x=1/4-6= -23/4
similarly Y=0 gives y=3
so the focus is (, 3)
we know that the equation of diretrix is X=-a
so, diretrix is
X=-1/4 but in new coordinate system i.e. XY system
or x+6=-1/4 in orig. system i.e. xy system