Identify correct statement(s) about conic \[ \sqrt{(x-5)^{2}+(y-7)^{2}}+\sqrt{(x+1)^{2}+(y+1)^{2...

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Identify correct statement(s) about conic
\[
\sqrt{(x-5)^{2}+(y-7)^{2}}+\sqrt{(x+1)^{2}+(y+1)^{2}}=12
\]
(a) Centre of conic is \( (2,3) \)
(b) Conic is hyperbola with foci \( (5,7) \) and \( (-1,-1) \)
(c) Conic is ellipse with major axis \( 4 x-3 y+1=0 \)
(d) Eccentricity of conic is \( \frac{5}{7} \)
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