A) \[x=y\]
B) \[x+y=0\]
C) \[x/{{a}^{2}}=y/{{b}^{2}}\]
D) \[x/{{a}^{2}}+y/{{b}^{2}}=0\]
Correct Answer: C
Solution :
The equation of chord having (x i,y,) as its mid-point is \[(x{{x}_{1}}/{{a}^{2}})+(y{{y}_{1}}/{{b}^{2}})-k=(x_{1}^{2}/{{a}^{2}})+(y_{1}^{2}/{{b}^{2}})-k\]\[\Rightarrow \]\[(x{{x}_{1}}/{{a}^{2}})+(y{{y}_{1}}/{{b}^{2}})=(x_{1}^{2}/{{a}^{2}})+(y_{1}^{2}/{{b}^{2}})\] It makes equal intercepts on the axes when \[({{a}^{2}}/{{x}_{1}})=({{b}^{2}}/{{y}_{1}})\Rightarrow ({{x}_{1}}/{{a}^{2}})-({{y}_{1}}/{{b}^{2}})=0\] Hence the locus of (x, y,) is (x/a2) = (y/b2 )
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