Answer to Question #270010 in Analytic Geometry for Angel Nodado

Question #270010

Identify the vertex, focus, axis of symmetry, directrix, direction of opening, length of the latus rectum, and the x- and y-intercepts of: 2y ^ 2 + x + 20y + 51 = 0


1
Expert's answer
2021-11-24T17:59:58-0500
2y2+x+20y+51=02y ^ 2 + x + 20y + 51 = 0

x=2(y2+10y+25)1x=-2(y ^ 2 +10y+25) -1

The equation of the parabola in vertex form:


x=2(y+5)21x=-2(y+5)^2-1

Vertex: (1,5)(-1, -5)


(y+5)2=4(18)(x+1)(y+5)^2=4(-\dfrac{1}{8})(x+1)

Focus: (118,5)=>(-1-\dfrac{1}{8}, -5)=>Focus: (98,5).(-\dfrac{9}{8}, -5).

Axis of symmetry: y=5.y=-5.

Directrix: x=1(18)=>x=-1-(-\dfrac{1}{8})=> Directrix: x=78.x=-\dfrac{7}{8}.

The horizontal parabola that opens to the left.

The length of the latus rectum of the parabola is 12.\dfrac{1}{2}.

x-intercept: (51,0)(−51,0)

No y-intercepts.



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