Given A circle, \( 2 x^{2}+2 y^{2}=5 \) and a parabola, \( y^{2}=4 \sqrt{5} x \). Statement I An...

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Given A circle, \( 2 x^{2}+2 y^{2}=5 \) and a parabola, \( y^{2}=4 \sqrt{5} x \).
Statement I An equation of a common tangent to
\( P \) these curves is \( y=x+\sqrt{5} \).

W
Statement II If the line, \( y=m x+\frac{\sqrt{5}}{m}(m \neq 0) \) is the commontangent, then \( m \) satisfies \( m^{4}-3 m^{2}+2=0 \).
(2013 Main)
(a) Statement \( \mathrm{I} \) is correct, Statement II is correct, Statement II is a correct explanation for Statement I
(b) Statement \( \mathrm{I} \) is correct, Statement II is correct, Statement II is not a correct explanation for Statement I
(c) Statement \( \mathrm{I} \) is correct, Statement II is incorrect
(d) Statement \( \mathrm{I} \) is incorrect, Statement II is correct
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