Exams Joint Entrance Examination Mathematics Circle Question 26 Question 26 of 219 Medium MCQ
Let the set of all values of r r r , for which the circles ( x + 1 ) 2 + ( y + 4 ) 2 = r 2 (x+1)^2+(y+4)^2=r^2 ( x + 1 ) 2 + ( y + 4 ) 2 = r 2 and x 2 + y 2 − 4 x − 2 y − 4 = 0 x^2+y^2-4 x-2 y-4=0 x 2 + y 2 − 4 x − 2 y − 4 = 0 intersect at two distinct points be the interval ( α , β ) (\alpha, \beta) ( α , β ) . Then α β \alpha \beta α β is equal to
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∣ r 1 − r 2 ∣ < c 1 c 2 < r 1 + r 2 r − 3 < 9 + 25 < r + 3 r ∈ ( 34 − 3 , 34 + 3 ) α β = 25 \begin{gathered} |{r}_{1}-{r}_{2}|<{c}_{1}{c}_{2}<{r}_{1}+{r}_{2} \\ r-3<\sqrt{9+25}<r+3 \\ r\in (\sqrt{34}-3,\sqrt{34}+3) \\ \alpha \beta =25 \end{gathered} ∣ r 1 − r 2 ∣ < c 1 c 2 < r 1 + r 2 r − 3 < 9 + 25 < r + 3 r ∈ ( 34 − 3 , 34 + 3 ) α β = 25 Answer the question to unlock