What is the minor radius of the ellipse $$\frac{(x+2)^2}{9}+\frac{(y-7)^2}{64}=1$$ ?


<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>What is the minor radius of the ellipse $$\frac{(x+2)^2}{9}+\frac{(y-7)^2}{64}=1$$ ?
</textarea>What is the minor radius of the ellipse <math><semantics><mrow><mfrac><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><msup><mo>)</mo><mn>2</mn></msup></mrow><mrow><mn>9</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mo>(</mo><mi>y</mi><mo>−</mo><mn>7</mn><msup><mo>)</mo><mn>2</mn></msup></mrow><mrow><mn>6</mn><mn>4</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\frac{(x+2)^2}{9}+\frac{(y-7)^2}{64}=1</annotation></semantics></math>​9​​(x+2)​2​​​​+​64​​(y−7)​2​​​​=1 ?
</div>

<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>Here the equation of the allipse,
$$(\frac{x+2}{3})^{2}+(\frac{y-7}{8})^{2}=1$$
Comparing with $$(\frac{x-h}{b})^{2}+(\frac{y-k}{a})^{2}=1$$ 
$$b=3$$
$$\therefore$$ Minor radius $$=3$$

</textarea>Here the equation of the allipse, <math><semantics><mrow><mo>(</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><msup><mo>)</mo><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>(</mo><mfrac><mrow><mi>y</mi><mo>−</mo><mn>7</mn></mrow><mrow><mn>8</mn></mrow></mfrac><msup><mo>)</mo><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">(\frac{x+2}{3})^{2}+(\frac{y-7}{8})^{2}=1</annotation></semantics></math>(​3​​x+2​​)​2​​+(​8​​y−7​​)​2​​=1 Comparing with <math><semantics><mrow><mo>(</mo><mfrac><mrow><mi>x</mi><mo>−</mo><mi>h</mi></mrow><mrow><mi>b</mi></mrow></mfrac><msup><mo>)</mo><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>(</mo><mfrac><mrow><mi>y</mi><mo>−</mo><mi>k</mi></mrow><mrow><mi>a</mi></mrow></mfrac><msup><mo>)</mo><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">(\frac{x-h}{b})^{2}+(\frac{y-k}{a})^{2}=1</annotation></semantics></math>(​b​​x−h​​)​2​​+(​a​​y−k​​)​2​​=1 <math><semantics><mrow><mi>b</mi><mo>=</mo><mn>3</mn></mrow><annotation encoding="application/x-tex">b=3</annotation></semantics></math>b=3 <math><semantics><mrow><mo>∴</mo></mrow><annotation encoding="application/x-tex">\therefore</annotation></semantics></math>∴ Minor radius <math><semantics><mrow><mo>=</mo><mn>3</mn></mrow><annotation encoding="application/x-tex">=3</annotation></semantics></math>=3
</div>