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  • A hyperbola has centre C and one focus at P(6, 8).  If its two directrices are <img alt="\mathrm{3 x+4 y+10=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B3%20x

A hyperbola has centre C and one focus at P(6, 8).  If its two directrices are \mathrm{3 x+4 y+10=0} and \mathrm{3 x+4 y-10=0} then CP=

Option: 1

14


Option: 2

8


Option: 3

10


Option: 4

6


Answers (1)

best_answer

\mathrm{\frac{2 a}{e}=4 \Rightarrow a=2 e}, P  is nearest to \mathrm{3 x+4 y-10=0 \Rightarrow a e-\frac{a}{e}=8 \Rightarrow e=\sqrt{5}, a=2 \sqrt{5}} \mathrm{C P=a e=10}

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Gautam harsolia

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