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ઉપવલય $25(x + 1)^2 + 9 (y + 2)^2 = 225$ ની નાભિના યામ મેળવો.
$(-1,2)$ અને $(-1, -6)$
$(-2, 1)$ અને $(-2, 6)$
$(-1, -2)$ અને $(-2, -1)$
$(-1, -2)$ અને $(-1, -6)$
Solution
$\frac{{{{\left( {x\,\, + \;\,1} \right)}^2}}}{{\frac{{225}}{{25}}}}\,\, + \;\,\frac{{{{\left( {y\,\, + \;\,2} \right)}^2}}}{{\frac{{225}}{9}}}\,\, = \,\,1$
$a\,\, = \,\,\sqrt {\frac{{225}}{{25}}} \,\, = \,\,\frac{{15}}{5},\,\,b\,\, = \,\sqrt {\frac{{225}}{9}\,} \,\,\, = \,\,\frac{{15}}{3}$
$\, \Rightarrow \,\,e\,\, = \,\,\sqrt {1\,\, – \,\,\frac{9}{{25}}} \,\, = \,\,\frac{4}{5}$
નાભિના યામ $ = \,\,\left( { – 1,\,\, – 2\, \pm \,\,\frac{{15}}{3}.\,\,\frac{4}{5}} \right)\,\,$
$= \,\,\left( { – 1,\,\, – 2\,\, \pm \,4} \right)\,\,\, = \,\,\left( { – 1,\,\,2} \right)\,;\,\,\left( { – 1,\,\, – 6} \right)$
