Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0.-4). Oy=-x?
Oy2 = -4x
Oy2 = -16%
Oyə tox?

Step-by-step explanation:

Given

Required

Equation of the parabola (in standard form)

The standard form of a parabola is

Such that

Vertex = (h,k)

Focus = (h, k + p)

For the vertex

This implies that (h,k) = (0,0)

h = 0 and k = 0

For the focus

This implies that (h, k + p) = (0, -4)

Recall that

Hence,

Substitute , in the given formula

becomes

Hence,, the standard form is

nothjing

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)