A) \[5{{x}^{2}}+3{{y}^{2}}=32\]
B) \[3{{x}^{2}}+5{{y}^{2}}=32\]
C) \[5{{x}^{2}}-3{{y}^{2}}=32\]
D) \[3{{x}^{2}}+5{{y}^{2}}+32=0\]
Correct Answer: B
Solution :
\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]. Since it passes through (?3, 1) and (2, ?2), so \[\frac{9}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=1\]and\[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{4}\]Þ\[{{a}^{2}}=\frac{32}{3}\], \[{{b}^{2}}=\frac{32}{5}\] Hence required equation of ellipse is\[3{{x}^{2}}+5{{y}^{2}}=32\]. Trick : Since only equation \[3{{x}^{2}}+5{{y}^{2}}=32\] passes through (?3, 1) and (2, ?2). Hence the result.
You need to login to perform this action.
You will be redirected in
3 sec
