What is the equation of the parabola with vertex

Ответ:

001234567891011

14.03.2022

$x=\frac{1}{12}(y-4)^{2}+2$

Step-by-step explanation:

In this problem we have that

The vertex and the focus has the same y-coordinate, therefore, is a horizontal parabola

The equation of a horizontal parabola is of the form

$x=a(y-k)^{2}+h$

where

(h,k) is the vertex

The coordinates of the focus are equal to $(h+\frac{1}{4a} ,k)$

we have in this problem

focus (5,4)

vertex (2,4)

substitute

(h,k)=(2,4)

$(5,4)=(2+\frac{1}{4a} ,4)$

Find the value of a

$5=2+\frac{1}{4a}\\ \\\frac{1}{4a}=3\\ \\a=\frac{1}{12}$

The equation of the horizontal parabola is equal to

$x=\frac{1}{12}(y-4)^{2}+2$ ------> open to the right

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