Conic sections: circles and parabolas

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Learn it A circle with centre (h, k) and radius r: (x − h)² + (y − k)² = r². From expanded form, complete the square in x and in y. A parabola x² = 4py has vertex (0, 0) and focus (0, p): satellite dishes and headlights use the focus.

Example: Centre and radius of x² + y² − 6x + 4y − 12 = 0?

(x − 3)² + (y + 2)² = 12 + 9 + 4 = 25.
Centre (3, −2), radius 5.

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