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3 years ago

PLZ HELP ASAP Geometry help: 2x^2 + 2y^2 - 8x +10y +2=0

1 answer:

6 0

Ok so this is conic sectuion
first group x's with x's and y's with y's
then complete the squra with x's and y's

2x^2-8x+2y^2+10y+2=0
2(x^2-4x)+2(y^2+5y)+2=0
take 1/2 of linear coeficient and square
-4/2=-2, (-2)^2=4
5/2=2.5, 2.5^2=6.25
add that and negative inside

2(x^2-4x+4-4)+2(y^2+5y+6.25-6.25)+2=0
factor perfect squares
2((x-2)^2-4)+2((y+2.5)^2-6.25)+2=0
distribute
2(x-2)^2-8+2(y+2.5)^2-12.5+2=0
2(x-2)^2+2(y+2.5)^2-18.5=0
add 18.5 both sides
2(x-2)^2+2(y+2.5)^2=18.5
divide both sides by 2
(x-2)^2+(y+2.5)^2=9.25

that is a circle center (2,-2.5) with radius √9.25

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Solution:

Let x be the age of April.

Laura's age = 2 years more than half of April's age

<u>Convert statement into algebraic expression:</u>

Half of April's age = $\frac{x}{2}$

2 years more than half of April's age = $\frac{x}{2}+2$

Combined age of April and Laura = 23

⇒ April's age + Laura's age = 23

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To add the fractions make the denominators same.

Multiplying 2 on both numerator and denominator of unlike terms, we get

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Denominators are same, now add the fractions.

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Do cross multiplication.

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$$\Rightarrow \ \ 3x=46-4$

$$\Rightarrow \ \ 3x=42$

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