A) \[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{24}=1\]
B) \[\frac{{{x}^{2}}}{24}-\frac{{{y}^{2}}}{25}=1\]
C) \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{25}=1\]
D) \[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{16}=1\]
E) \[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{24}=-1\]
Correct Answer: A
Solution :
Vertices of hyperbola are\[(a,0),(-a,0)\] Given vertices\[(5,0),\text{ }(-5,0)\] \[\therefore \] \[a=5\] Also one of the directrix let \[x=\frac{a}{e}\]is given as \[x=\frac{25}{7}\] \[\Rightarrow \] \[e=\frac{7}{5}\] \[\therefore \] \[{{b}^{2}}={{a}^{2}}({{e}^{2}}-1)=25\left( \frac{49}{25}-1 \right)=24\] \[\therefore \] Equation hyperbola is \[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{24}=1\]
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