Consider conic C , ,: , ,25 ( x - 1 )^2 + ,25 ( y + 1 )^2 = , ( 3… - Vidyadip

Question

Consider conic $C\,\,:\,\,25{\left( {x - 1} \right)^2} + \,25{\left( {y + 1} \right)^2} = \,{\left( {3x\, - \,4y} \right)^2}$ . If curve $E$ is locus of point of intersection of perpendicular tangents to the conic $C$ , then minimum distance between curve $E$ and point $(2,-1)$ is

✓

Answer

b
Given conic $\mathrm{C}$ is parabola

focus : $(1,-1)$

$\mathrm{E}: 3 \mathrm{x}-4 \mathrm{y}=0$

minimum distance is $\perp$ distance

$\Rightarrow$ distance $=\left|\frac{6+4}{5}\right|=2$

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