Interval of r for which x2 + y2 = r2 and x2 + y2 - 6x -8y + 9 = 0 cut at two distinct points is
(1) (2.12)
(2) (2, 10)
(3) (1.8)
(4) (1,9)
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Interval of r = (1,9) for which x² + y² = r² & x² + y² - 6x - 8y + 9 = 0 cut at two distinct points
Step-by-step explanation:
x² + y² = r²
Center = (0,0)
radius = r
x² + y² - 6x - 8y + 9 = 0
=> (x - 3)² - 9 + (y - 4)² - 16 + 9 = 0
=> (x - 3)² + (y - 4)² = 16
=> (x - 3)² + (y - 4)² = 4²
Center =( 3, 4) & Radius = 4
cut at two distinct points is
=> | r - 4 | < √((4-0)² + (3 - 0)² ) < | r + 4|
=> | r - 4| < 5 < r + 4
=> r < 9 & r > 1
=> Interval of r = (1,9)
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