A) \[-r\sqrt{1+{{m}^{2}}}<c<r\sqrt{1+{{m}^{2}}}\]
B) \[-r<c<r\]
C) \[-r\sqrt{1-{{m}^{2}}}<c<r\sqrt{1+{{m}^{2}}}\]
D) None of these
Correct Answer: A
Solution :
[a] Given line is \[y=mx+c\] ? (1) and the given circle is \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\] ? (2) Solving (1) and (2), we get \[(1+{{m}^{2}}){{x}^{2}}+2mcx+{{c}^{2}}-{{r}^{2}}=0\] ?. (3) For two real distinct points of intersection, both the roots of (3) must be real distinct. \[\therefore \,\,\,\,\,4{{m}^{2}}{{c}^{2}}-4(1+{{m}^{2}})({{c}^{2}}-{{r}^{2}})>0\] \[\Rightarrow {{c}^{2}}<{{r}^{2}}(1+{{m}^{2}})\Rightarrow \] \[-r\sqrt{1+{{m}^{2}}}<c<\sqrt{1+{{m}^{2}}}\]
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