A) \[\left( \frac{a}{\sqrt{2}},\frac{a}{\sqrt{2}} \right)\]
B) \[\left( -\frac{a}{\sqrt{2}},-\frac{a}{\sqrt{2}} \right)\]
C) \[\left( \frac{a}{\sqrt{2}},-\frac{a}{\sqrt{2}} \right)\]
D) \[\left( -\frac{a}{\sqrt{2}},\frac{a}{\sqrt{2}} \right)\]
Correct Answer: D
Solution :
Suppose that the point be (h, k). Tangent at (h, k) is \[hx+ky={{a}^{2}}\equiv x-y=-\sqrt{2}a\] or \[\frac{h}{1}=\frac{k}{-1}=\frac{{{a}^{2}}}{-\sqrt{2}a}\] or \[h=-\frac{a}{\sqrt{2}},\ k=\frac{a}{\sqrt{2}}\] Therefore, point of contact is \[\left( -\frac{a}{\sqrt{2}},\ \frac{a}{\sqrt{2}} \right)\].
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