A) \[y=\sqrt{3}x\pm \sqrt{3{{a}^{2}}+{{b}^{2}}}\]
B) \[y=\pm x+\sqrt{{{a}^{2}}+{{b}^{2}}}\]
C) \[y=\sqrt{3x}\pm +\sqrt{{{a}^{2}}+3{{b}^{2}}}\]
D) None of the above
Correct Answer: B
Solution :
Let equations of line which cut equal intercepts are \[y\pm x=\pm c\] or \[y=\pm \text{ }x\pm c\] Since, it is a tangent of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[\therefore \] \[c=\sqrt{{{a}^{2}}+{{b}^{2}}}\] Hence, required equation of line is \[y=\pm x+\sqrt{{{a}^{2}}+{{b}^{2}}}\]
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