SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Algebra, SPEC2 2011 VCAA 2 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

A.   −3 and 38

B.   3 and 12

C.   −3 and −8

D.   −3 and 0

E.   3 and 18

Show Answers Only

`B`

Show Worked Solution
`x^2 – 6x + y^2 + 4y` `=b`
`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`