Math, asked by hxisnan, 10 months ago

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)​

Answers

Answered by amitnrw
9

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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Answered by kapishgupta2406
0

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