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If necessary, use / for the fraction bar. 6and the focus (3,-5),what is the vertex form of the equation of the parabola? Given the directrix U The vertex form of the equation is a = SH Meny 4² (y +?

If necessary use for the fraction bar 6and the focus 35what is the vertex form of the equation of the parabola Given the directrix U The vertex form of the equ class=

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SOLUTION:

Directrix is the line x = 6 ;

Focus is the point (3,-5).

Thus, the focal length is

[tex]\frac{6-3}{2}=1.5[/tex]

The vertex is ( 4.5 , -5 )

The equation of such a parabola that opens leftward is;

[tex]\begin{gathered} x=-\frac{1}{4p}(y-k)^2+h \\ x=-\frac{1}{4\times1.5}(y-(-5))^2+4.5 \end{gathered}[/tex]

Simplified as;

[tex]x=-\frac{1}{6}(y+5)^2+4.5[/tex]

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