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Pavel [41]
2 years ago
15

Can anyone tell me the standard form of this parabola equation?

Mathematics
1 answer:
irina [24]2 years ago
7 0

Answer:

x=4y^2-24y+30

(x-4.5)^2+(y-2.5)^2=23

Step-by-step explanation:

Standard form of a sideways parabola:  x=ay^2+by+c

Given equation:

4y^2-x-24y+30=0

Add x to both sides:

4y^2-24y+30=x

\implies x=4y^2-24y+30

--------------------------------------------------------------------------------------------

<u>Standard form of circle equation</u>

(x-a)^2+(y-b)^2=r^2

(where (a,b) is the center and r is the radius)

Given equation:

2x^2+2y^2-18x-10y+7=0

Group like terms:

2x^2-18x+2y^2-10y+7=0

Divide by 2:

x^2-9x+y^2-5y+3.5=0

Factor by completing the square for each variable:

(x-4.5)^2-20.25+(y-2.5)^2-6.25+3.5=0

Rearrange into standard form:

(x-4.5)^2+(y-2.5)^2=23

Therefore, the circle has a center at (4.5, 2.5) and a radius of √23

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