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  • The range of values of a for which the point is outside the circles <img alt="x^2+y^2+10 x=0" src="https://

The range of values of a for which the point (a, 4) is outside the circles x^2+y^2+10 x=0 and

x^2+y^2-12 x+20=0 is

Option: 1

(-\infty,-8) \cup(-2,6) \cup(6,+\infty)


Option: 2

(-8,-2)


Option: 3

(-\infty,-8) \cup(-2,+\infty)


Option: 4

\mathrm{None \, \, of \, \, these}


Answers (1)

best_answer

For circle, x^2+y^2+10 x=0 \text {; }

a^2+(4)^2+10 a>0 \Rightarrow a^2+10 a+16>0 \Rightarrow(a+8)(a+2)>0   \Rightarrow a<-8 \text { or } a>-2      .....(i)

For circle,   x^2+y^2-12 x+20=0 ; a^2+(4)^2-12 a+20>0 \Rightarrow a^2-12 a+36>0

\Rightarrow(a-6)^2>0 \Rightarrow a \in R_{\sim}\{6\}                     ...(ii)

Taking common values from (i) and (ii),

a \in(-\infty,-8) \cup(-2,6) \cup(6,+\infty)

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Gaurav

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