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  • The asymptotes of a hyperbola   <img alt="\mathrm{\frac{x^2}{a_1^2}-\frac{y^2}{b_1^2}=1 \text { and } \frac{x^2}{a_2^2}-\frac{y^2}{b_2^2}=1}" src="https://entrancecorner.oncodecogs.c

The asymptotes of a hyperbola   \mathrm{\frac{x^2}{a_1^2}-\frac{y^2}{b_1^2}=1 \text { and } \frac{x^2}{a_2^2}-\frac{y^2}{b_2^2}=1}

are perpendicular to each other. Then,

Option: 1

\mathrm{a_1 / a_2=b_1 / b_2}


Option: 2

\mathrm{a_1a_2=b_1b_2}


Option: 3

\mathrm{a_1a_2+b_1b_2}


Option: 4

\mathrm{a_1-a_2=b_1-b_2}


Answers (1)

best_answer

The slopes of asymptotes are

\mathrm{m_1=\frac{b_1}{a_1}, m_2=\frac{b_2}{a_2}}

According to the question,

\mathrm{\begin{aligned} & m_1 m_2=-1 \\ & a_1 a_2+b_1 b_2=0 \end{aligned}}

Posted by

seema garhwal

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