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(y+4)^(2)=-6(x-2) Which conic section...

`(y+4)^(2)=-6(x-2)`
Which conic section does this define? Also find, if they exist,
(i) the center
(ii) the vertex/vertices
(iii) the focus/foci
(iv) the directrix
(v) the asymtotes
(vi) the eccentricity

Text Solution

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This is a parabola with an x-orientaiton opening left. In this problem `h=2,k=-4andp=-(3)/(2)`
(i) A parabola does not have a center.
(ii) The vertex is (2,-4).
(iii) The focus is `((1)/(2),-4)`
(iv) The directrix is `x=(7)/(2)`
(v) A parabola does not have asymptotes.
(vi) The eccentricity of a parabola is 1.
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