If P(a, b) is the centre of circle touching y-axis and
the lines y = x + 5 and y = x - 1. Then the product of
possible values of (a + b) is
Answers
-14 is product of possible values of (a + b)
Step-by-step explanation:
P(a, b) is the centre of circle touching y-axis
radius² = a²
=> radius = | a |
P(a, b) is the centre of circle touching the lines y = x + 5
=> x - y + 5 = 0
radius = | a - b + 5|/√2
P(a, b) is the centre of circle touching the lines y = x -1
=> x - y - 1 = 0
radius = | a - b - 1|/√2
| a - b + 5|/√2 = | a - b - 1|/√2
=> | a - b + 5| = | a - b - 1|
=> a - b = - 2
radius = | a - b + 5|/√2 = 3/√2
| a | = 3/√2
=> a = ± 3/√2
a - b = - 2
=> b = a + 2
b = 2 ± 3/√2
(a + b) = 3/√2 + 2 + 3/√2 or -3/√2 + 2 - 3/√2
= 2 + 3√2 or 2 - 3√2
(2 + 3√2)(2 - 3√2)
= 4 - 18
= - 14
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