A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is :
JEE · Math · previous-year question
- A.$$y = \sqrt 2 x$$
- B.$$x = \sqrt 2 y$$
- C.$${y^2} - {x^2} = 2xy$$
- D.$${x^2} - {y^2} = 2xy$$correct
Answer
D. $${x^2} - {y^2} = 2xy$$
Explanation
Let the centre be (h, k) So, $$\left| h \right| = \left| {{{h + k} \over {\sqrt 2 }}} \right|$$ $$ \Rightarrow 2{h^2} = {h^2} + {k^2} + 2hk$$ Locus will be $${x^2} - {y^2} = 2xy$$
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