MCQ
ઉપવલય $9{{x}^{2}}+16{{y}^{2}}-90x+32y+97={0}$ નું કેન્દ્ર ............. .
- ✓$\left( 5,-1 \right)$
- B$\left( 5,1 \right)$
- C$\left( 1,5 \right)$
- D$\left( 1,-5 \right)$
ઉપવલય $9{{x}^{2}}+16{{y}^{2}}-90x+32y+97= {0} $
$\therefore 9{{x}^{2}}+16{{y}^{2}}-90x+225+32y+16+97-241= {0} $
$\therefore 9(x^2-10x+25)+16(y^2+2y+1)=144$
$\therefore \frac{(x-5)^2}{16}+\frac{(y+1)^2}{9}=1$
ઉપવલય નું કેન્દ્ર $ = (5,-1)$
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$\frac{{{x^2}}}{{144}}\,\, - \,\,\frac{{{y^2}}}{{81}}\,\, = \,\,\frac{1}{{25}}$ ની નાભીઓ સમાન હોય તો ${b^2}$ નું મૂલ્ય: