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PART - 2 CH - 10 Conic Sections — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPART - 2 CH - 10 Conic Sections1 Mark
Question
Write the equation of hyperbola whose transverse axis and conjugate axis are 4 and 5 respectively.
✓

Answer


$\begin{array}{l} \text { Given that : } \quad 2 a=4, \quad 2 b=5 \\ \Rightarrow \quad a=2 \quad \Rightarrow \quad b=\frac{5}{2} \\ \Rightarrow \$a)^2=4 \quad \text { and } b^2=\frac{25}{4} \end{array}$
So, equation of hyperbola :
$\begin{array}{lc} \Rightarrow & \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \\ \Rightarrow & \frac{x^2}{4}-\frac{y^2}{\frac{25}{4}}=1 \\ \Rightarrow & \frac{x^2}{4}-\frac{4 y^2}{25}=1 \\ \Rightarrow & 25 x^2-16 y^2=100 \end{array}$

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