Answer to Question #270010 in Analytic Geometry for Angel Nodado

Question

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

Answer 1

$$2y ^ 2 + x + 20y + 51 = 0$$

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

The equation of the parabola in vertex form:

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

Vertex: $(-1, -5)$

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

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

Axis of symmetry: $y=-5.$

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

The horizontal parabola that opens to the left.

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

x-intercept: $(−51,0)$

No y-intercepts.