What is the center of the circle x^2 + y^2 + 3x + 4y = 45
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The equation of a circle with radius r and center (h, k) is (x - h)^2 + (y - k)^2 = r^2.
Express the equation of the circle given in the form described.
x^2 + y^2 + 3x + 4y = 45
=> x^2 + 3x + y^2 + 4y = 45
=> x^2 + 3x + (3/2)^2 + y^2 + 4y + 4 = 45 + 9/4 + 4
=> (x + 3/2)^2 + (y + 2)^2 = 205/4
The center of the circle is (-3/2, -2)
`A)` You can re-write the eqaution as:
So the circle has the centre in the point C(2;-3)
`B)` to se if the point A(6-6) lies on the cirlce is enough to see if the distance d from the center C(2,-3) is R.
The the point lies on the circle.
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