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The circle of `x^2-6x + y^2 + 4y-3 = 0` is reflected in the `x`-axis.
Sketch the reflected circle, showing the coordinates of the centre and the radius. (3 marks)
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| `x^2-6x + y^2 + 4y-3` | `= 0` |
| `x^2-6x + 9 + y^2 + 4y + 4-16` | `= 0` |
| `(x-3)^2 + (y + 2)^2` | `= 16` |
`=>\ text{Original circle has centre (3, − 2), radius = 4}`
`text(Reflect in)\ xtext(-axis):`
`text{Centre (3, − 2) → (3, 2)}`
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 18
Sketch the graph of `(x-3)^2 + (y + 2)^2 = 4.` (2 marks)
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`(x-3)^2 + (y + 2)^2 = 4\ \ text(is a circle),`
`text(centre)\ (3, -2),\ text(radius 2.)`
Write down the equation of the circle with centre `(-1, 2)` and radius 5. (1 mark)