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Answer :
Sure! Let's solve the problem step by step to isolate [tex]\( y^2 \)[/tex] from the given equation:
The original equation is:
[tex]\[ 4x^2 + 25y^2 = 100 \][/tex]
1. Subtract [tex]\( 4x^2 \)[/tex] from both sides:
To start isolating [tex]\( y^2 \)[/tex], we need to remove the [tex]\( 4x^2 \)[/tex] term on the left side. We do this by subtracting [tex]\( 4x^2 \)[/tex] from both sides of the equation:
[tex]\[ 25y^2 = 100 - 4x^2 \][/tex]
2. Divide by 25:
Now, to solve for [tex]\( y^2 \)[/tex], divide both sides of the equation by 25 to isolate [tex]\( y^2 \)[/tex]:
[tex]\[
y^2 = \frac{100 - 4x^2}{25}
\][/tex]
3. Simplify the expression:
Divide each term in the numerator by 25:
[tex]\[
y^2 = \frac{100}{25} - \frac{4x^2}{25}
\][/tex]
Simplify each term:
[tex]\[
y^2 = 4 - \frac{4}{25}x^2
\][/tex]
The final result for [tex]\( y^2 \)[/tex] is:
[tex]\[ y^2 = 4 - \frac{4}{25}x^2 \][/tex]
The correct option is A: [tex]\( y^2 = 4 - \frac{4}{25}x^2 \)[/tex]
The original equation is:
[tex]\[ 4x^2 + 25y^2 = 100 \][/tex]
1. Subtract [tex]\( 4x^2 \)[/tex] from both sides:
To start isolating [tex]\( y^2 \)[/tex], we need to remove the [tex]\( 4x^2 \)[/tex] term on the left side. We do this by subtracting [tex]\( 4x^2 \)[/tex] from both sides of the equation:
[tex]\[ 25y^2 = 100 - 4x^2 \][/tex]
2. Divide by 25:
Now, to solve for [tex]\( y^2 \)[/tex], divide both sides of the equation by 25 to isolate [tex]\( y^2 \)[/tex]:
[tex]\[
y^2 = \frac{100 - 4x^2}{25}
\][/tex]
3. Simplify the expression:
Divide each term in the numerator by 25:
[tex]\[
y^2 = \frac{100}{25} - \frac{4x^2}{25}
\][/tex]
Simplify each term:
[tex]\[
y^2 = 4 - \frac{4}{25}x^2
\][/tex]
The final result for [tex]\( y^2 \)[/tex] is:
[tex]\[ y^2 = 4 - \frac{4}{25}x^2 \][/tex]
The correct option is A: [tex]\( y^2 = 4 - \frac{4}{25}x^2 \)[/tex]
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