(6p+5q)2=36p^2+25q^2

解

(6 p + 5 q) 2 = 36 p^{2} + 25 q^{2}

(h, k) = (\frac{1}{6}, \frac{1}{5}), a = \frac{1}{3 2}, b = \frac{2}{5}

解答ステップ

(6 p + 5 q) \cdot 2 = 36 p^{2} + 25 q^{2}

(6 p + 5 q) 2 - 36 p^{2} - 25 q^{2} = 0

を標準的な楕円のequationの形式で書き換える

\frac{( p - \frac{1}{6} ) ^{2}}{( \frac{1}{3 2} ) ^{2}} + \frac{( q - \frac{1}{5} ) ^{2}}{( \frac{2}{5} ) ^{2}} = 1

ゆえに楕円の特性は:

(h, k) = (\frac{1}{6}, \frac{1}{5}), a = \frac{1}{3 2}, b = \frac{2}{5}

b > a

ゆえに

b

は半長径,

a

は半短径である

中心が (h, k) = (\frac{1}{6}, \frac{1}{5}), b = \frac{2}{5}, a = \frac{1}{3 2} の楕円