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Question

What is the equation of a curve given by the parametric form x=9+6 sec θ;y= 24 tanθ.


A

^2}{36}-\frac{(y-2)^2}{16}=1\)

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B

^2}{36}-\frac{(y+2)^2}{16}=1\)

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C

^2}{81}-\frac{(y+4)^2}{4}=1\)

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D

^2}{81}-\frac{(y-4)^2}{4}=1\)

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Solution

The correct option is B

^2}{36}-\frac{(y+2)^2}{16}=1\)


Given parametric equation are,

x=9+6 sec θ

y=24 tan θ

Eliminating θ from these

sec2θtan2θ=1

i.e., (x96)2(y+24)2=1

(x9)236(y+2)216=1


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