A) \[y=\sqrt{3}x\pm \sqrt{3{{a}^{2}}+{{b}^{2}}}\]
B) \[y=\pm x\mp \sqrt{{{a}^{2}}+{{b}^{2}}}\]
C) \[y=\sqrt{3}\pm \sqrt{{{a}^{2}}+3{{b}^{2}}}\]
D) None of the above
Correct Answer: B
Solution :
Let the equation of line of equal intercept is \[y\pm x=\pm c\] \[y=\pm x\mp c\] Since, this line is tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[\therefore \] \[c=\sqrt{{{a}^{2}}+{{b}^{2}}}\] \[\therefore \]Required line is \[y=\pm x\mp \sqrt{{{a}^{2}}+{{b}^{2}}}\] Hence, option is correct.
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