Solution :
\(\because\) Equation of ellipse is \(9x^2 + 16y^2\) = 144 or \(x^2\over 16\) + \({(y-3)}^2\over 9\) = 1
comparing this with \(x^2\over a^2\) + \(y^2\over b^2\) = 1 then we get \(a^2\) = 16 and \(b^2\) = 9
and comparing the line y = x + k with y = mx + c ; m = 1 and c = k
If the line y = x + k touches the ellipse \(9x^2 + 16y^2\) = 144, then \(c^2\) = \(a^2m^2 + b^2\)
\(\implies\) \(k^2\) = 16 \(\times\) \(1^2\) + 9 \(\implies\) \(k^2\) = 25
\(\therefore\) k = \(\pm\)5
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The foci of an ellipse are \((\pm 2, 0)\) and its eccentricity is 1/2, find its equation.