Let the set of all values of r, for which the circles (x+1 )^2+ (y+4 )^2=r^2 and x^2+y^2-4x-2y-4=0 intersect at two distinct points be the interval ( , ). Then αβ is equal to

Question

Accepted Answer

Correct answer: D. (d) Circle 1: center C_1= (-1 ,-4 ), radius r. Circle 2: (x-2 )^2+ (y-1 )^2=9, center C_2= (2 ,1 ), radius 3 . Distance d= 9+25= 34. For two intersection points: |r-3 |< 34 34 ⇒r> 34-3 and |r-3 |< 34 ⇒r< 34+3. r ∈ ( 34-3 , 34+3 ), so = 34-3 , = 34+3. αβ= ( 34 )^2-9=34-9=25.

$Let the set of all values of r, for which the circles (x + 1)^{2} + (y + 4)^{2} = r^{2} and x^{2} + y^{2} - 4 x - 2 y - 4 = 0 intersect at two distinct points be the interval (α, β) . Then αβ is equal to$

Solution

More Circle PYQs