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Answer :
Let's solve the problem step by step to isolate [tex]\( y^2 \)[/tex] in the given equation.
The original equation is:
[tex]\[ 4x^2 + 25y^2 = 100 \][/tex]
Step 1: Move the [tex]\( 4x^2 \)[/tex] term to the right side of the equation.
We do this by subtracting [tex]\( 4x^2 \)[/tex] from both sides:
[tex]\[ 25y^2 = 100 - 4x^2 \][/tex]
Step 2: Solve for [tex]\( y^2 \)[/tex] by dividing everything by 25.
To isolate [tex]\( y^2 \)[/tex], divide each term of the equation by 25:
[tex]\[ y^2 = \frac{100}{25} - \frac{4x^2}{25} \][/tex]
Simplify the fractions:
[tex]\[ y^2 = 4 - \frac{4}{25}x^2 \][/tex]
The correct answer is:
A. [tex]\( y^2 = 4 - \frac{4}{25}x^2 \)[/tex]
The original equation is:
[tex]\[ 4x^2 + 25y^2 = 100 \][/tex]
Step 1: Move the [tex]\( 4x^2 \)[/tex] term to the right side of the equation.
We do this by subtracting [tex]\( 4x^2 \)[/tex] from both sides:
[tex]\[ 25y^2 = 100 - 4x^2 \][/tex]
Step 2: Solve for [tex]\( y^2 \)[/tex] by dividing everything by 25.
To isolate [tex]\( y^2 \)[/tex], divide each term of the equation by 25:
[tex]\[ y^2 = \frac{100}{25} - \frac{4x^2}{25} \][/tex]
Simplify the fractions:
[tex]\[ y^2 = 4 - \frac{4}{25}x^2 \][/tex]
The correct answer is:
A. [tex]\( y^2 = 4 - \frac{4}{25}x^2 \)[/tex]
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