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Answer :
To isolate [tex]\( y^2 \)[/tex] in the equation [tex]\( 4x^2 + 25y^2 = 100 \)[/tex], follow these steps:
1. Rearrange the equation:
Start by moving the term [tex]\( 4x^2 \)[/tex] to the other side of the equation:
[tex]\[
25y^2 = 100 - 4x^2
\][/tex]
2. Solve for [tex]\( y^2 \)[/tex]:
To isolate [tex]\( y^2 \)[/tex], divide every term by 25:
[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]
[tex]\[
y^2 = 4 - \frac{4}{25}x^2
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{y^2 = 4 - \frac{4}{25} x^2}
\][/tex]
However, none of the provided options directly match this form as needed based on the Python verification. So it's possible there is an error in the options listing or misalignment with the options provided.
1. Rearrange the equation:
Start by moving the term [tex]\( 4x^2 \)[/tex] to the other side of the equation:
[tex]\[
25y^2 = 100 - 4x^2
\][/tex]
2. Solve for [tex]\( y^2 \)[/tex]:
To isolate [tex]\( y^2 \)[/tex], divide every term by 25:
[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]
[tex]\[
y^2 = 4 - \frac{4}{25}x^2
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{y^2 = 4 - \frac{4}{25} x^2}
\][/tex]
However, none of the provided options directly match this form as needed based on the Python verification. So it's possible there is an error in the options listing or misalignment with the options provided.
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