Convert the following equation of ellipse into standard from .
(i) `16x^(2)+9y^(2)=144`
(ii) `9x^(2)+25y^(2)=225`

Answer

To convert the given equations of ellipses into standard form, we will follow a systematic approach.

### Solution Steps:

#### (i) For the equation \( 16x^2 + 9y^2 = 144 \):

1. **Divide the entire equation by 144**:
\[ \frac{16x^2}{144} + \frac{9y^2}{144} = \frac{144}{144} \]

2. **Simplify each term**:
\[ \frac{16}{144}x^2 + \frac{9}{144}y^2 = 1 \]
This simplifies to:
\[ \frac{1}{9}x^2 + \frac{1}{16}y^2 = 1 \]

3. **Rewrite in standard form**:
\[ \frac{x^2}{3^2} + \frac{y^2}{4^2} = 1 \]

Thus, the standard form of the ellipse is:
\[ \frac{x^2}{9} + \frac{y^2}{16} = 1 \]

#### (ii) For the equation \( 9x^2 + 25y^2 = 225 \):

1. **Divide the entire equation by 225**:
\[ \frac{9x^2}{225} + \frac{25y^2}{225} = \frac{225}{225} \]

2. **Simplify each term**:
\[ \frac{9}{225}x^2 + \frac{25}{225}y^2 = 1 \]
This simplifies to:
\[ \frac{1}{25}x^2 + \frac{1}{9}y^2 = 1 \]

3. **Rewrite in standard form**:
\[ \frac{x^2}{5^2} + \frac{y^2}{3^2} = 1 \]

Thus, the standard form of the ellipse is:
\[ \frac{x^2}{25} + \frac{y^2}{9} = 1 \]

### Final Answers:
1. \( \frac{x^2}{9} + \frac{y^2}{16} = 1 \)
2. \( \frac{x^2}{25} + \frac{y^2}{9} = 1 \)