A) \[9{{x}^{2}}+25{{y}^{2}}=225\]
B) \[25{{x}^{2}}+9{{y}^{2}}=225\]
C) \[3{{x}^{2}}+4{{y}^{2}}=192\]
D) None of these
Correct Answer: A
Solution :
Given, vertex\[(\pm 5,0)=(\pm \text{ }a,0)\] \[\Rightarrow \] \[a=5\] and focus\[(\pm 4,0)=(\pm \text{ }ae,0)\] \[\Rightarrow \] \[ae=4\] \[\Rightarrow \] \[e=\frac{4}{a}=\frac{4}{5}\] \[\therefore \] \[b=\sqrt{{{a}^{2}}(1-{{e}^{2}})}\] \[\Rightarrow \] \[b=\sqrt{25\frac{(25-16)}{25}}\] \[\Rightarrow \] \[b=\sqrt{9}\] \[\Rightarrow \] \[b=3\] Hence, equation is\[\frac{{{x}^{2}}}{{{(5)}^{2}}}+\frac{{{y}^{2}}}{{{(3)}^{2}}}=1\] \[\Rightarrow \] \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{9}=1\] \[\Rightarrow \] \[9{{x}^{2}}+25{{y}^{2}}=225\]
You need to login to perform this action.
You will be redirected in
3 sec
