A) (?6, ?9)
B) (?13, ?9)
C) (?6, ?7)
D) (13, 7)
Correct Answer: C
Solution :
Equation of tangent at (1, 7) to \[y={{x}^{2}}+6\] \[\frac{1}{2}(y+7)=x.1+6\] Þ \[y=2x+5\] ?..(i) This tangent also touches the circle \[{{x}^{2}}+{{y}^{2}}+16x+12y+c=0\] ?..(ii) Now solving (i) and (ii), we get Þ\[{{x}^{2}}+{{(2x+5)}^{2}}+16x+12(2x+5)+c=0\] Þ\[5{{x}^{2}}+60x+85+c=0\] Since, roots are equal so \[{{b}^{2}}-4ac=0\] Þ \[{{(60)}^{2}}-4\times S\times (85+c)=0\] Þ \[85+c=180\] Þ \[5{{x}^{2}}+60x+180=0\] Þ \[x=-\frac{60}{10}=-6\] Þ \[y=-7\] Hence, point of contact is (?6, ?7).
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