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Circles and Hyperbolas, SMB-010 MC

A circle with centre `(a,-2)` and radius 5 units has equation

`x^2-6x + y^2 + 4y = b`  where  `a`  and  `b`  are real constants.

The values of  `a`  and  `b`  are respectively

  1. −3 and 38
  2. 3 and 12
  3. −3 and −8
  4. 3 and 18
Show Answers Only

`B`

Show Worked Solution

`x^2-6x + y^2 + 4y=b`

`text(Completing the squares:)`

`x^2-6x + 3^2-9 + y^2 + 4y + 2^2-4` `= b`
`(x-3)^2 + (y + 2)^2-13` `= b`
`(x-3)^2 + (y + 2)^2` `= b + 13`

 
`:. a=3`

`:. b+13=25\ \ =>\ \ b=12`

`=> B`