If a variable line, 3x+4y–
=0 is such that the two circles x2 + y2 – 2x – 2y + 1 = 0 and x2+y2–18x–2y+78 = 0 are on its opposite sides, then the set of all values of is the interval
a.
[12,21]
b.
(2, 17)
c.
(23 , 31)
d.
[13, 23]
=0 is such that the two circles x2 + y2 – 2x – 2y + 1 = 0 and x2+y2–18x–2y+78 = 0 are on its opposite sides, then the set of all values of is the intervala.
[12,21]
b.
(2, 17)
c.
(23 , 31)
d.
[13, 23]
Question ID - 57194 | SaraNextGen Top Answer If a variable line, 3x+4y–=0 is such that the two circles x2 + y2 – 2x – 2y + 1 = 0 and x2+y2–18x–2y+78 = 0 are on its opposite sides, then the set of all values of is the interval
a.
[12,21]
b.
(2, 17)
c.
(23 , 31)
d.
[13, 23]
If a variable line, 3x+4y–=0 is such that the two circles x2 + y2 – 2x – 2y + 1 = 0 and x2+y2–18x–2y+78 = 0 are on its opposite sides, then the set of all values of is the interval
|
a. |
[12,21] |
b. |
(2, 17) |
|
c. |
(23 , 31) |
d. |
[13, 23] |
1 Answer
127 votes
Answer Key / Explanation : (a) -
Centre of circles are opposite side of line
(3 + 4 − 
) (27 + 4 − 
) < 0
(
− 7) ( − 31) < 0
(7, 31)
distance from S1
≥ 1
⇒ λ 
(−
, 2] 
[12, 
)
distance from S2
≥ 2
⇒ 
(−
, 21] 
[41, 
)
So 
[12, 21]
127 votes
Answer Link
127