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  • If  <img alt="\mathrm{(13 x-1)^2+(13 y-2)^2=c(5 x+12 y-1)^2}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%2813%20x-1%29%5E2&plus;%2813%20y-2%29%5E2%3Dc%285%20xa

If  \mathrm{(13 x-1)^2+(13 y-2)^2=c(5 x+12 y-1)^2}represents an ellipse , then set of 

value of \mathrm{c} is

Option: 1

\mathrm{(1, \infty)}


Option: 2

(0,1)


Option: 3

1


Option: 4

none of these


Answers (1)

best_answer

Here  \mathrm{\left(x-\frac{1}{13}\right)^2+\left(y-\frac{2}{13}\right)^2=c\left(\frac{5 x+12 y-1}{13}\right)^2}

Now from definition focus is \mathrm{\left(\frac{1}{13}, \frac{2}{13}\right)}  , Directrix is \mathrm{5 x+12 y-1=0 \text { and } c} is

same as square of eccentricity which belongs to  \mathrm{(0,1) \text {. }}

Posted by

Anam Khan

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