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Home » Find the equations of the hyperbola satisfying the given conditions. Vertices (±2, 0), foci (±3, 0)
Find the equations of the hyperbola satisfying the given conditions. Vertices (±2, 0), foci (±3, 0)
CBSE | Class 11 | Conic Sections | Exercise 11.4 | Maths | NCERT
Find the equations of the hyperbola satisfying the given conditions. Vertices (±2, 0), foci (±3, 0)

Given:

    \[Vertices\text{ }\left( \pm 2,\text{ }0 \right)\text{ }and\text{ }foci\text{ }\left( \pm 3,\text{ }0 \right)\]

Here, the vertices are on the

    \[x-axis\]

Along these lines, the condition of the hyperbola is of the structure

    \[~{{x}^{2}}/{{a}^{2}}~\text{ }{{y}^{2}}/{{b}^{2}}~=\text{ }1\]

Since, the vertices are

    \[\left( \pm 2,\text{ }0 \right),\]

along these lines,

    \[a\text{ }=\text{ }2\]

Since, the foci are

    \[\left( \pm 3,\text{ }0 \right),~\]

in this way,

    \[c\text{ }=\text{ }3\]

It is realize that,

    \[{{a}^{2}}~+\text{ }{{b}^{2}}~=\text{ }{{c}^{2}}\]

In this way,

    \[{{2}^{2}}~+\text{ }{{b}^{2}}~=\text{ }{{3}^{2}}\]

    \[{{b}^{2}}~=\text{ }9\text{ }\text{ }4\text{ }=\text{ }5\]

∴ The condition of the hyperbola is

    \[{{x}^{2}}/4\text{ }\text{ }{{y}^{2}}/5\text{ }=\text{ }1\]

i

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