Question

A circle has the equation x2+ 12x+y2 -8y = 73.
(a) Determine the coordinates of the center of the circle. Show how you arrived at
your answer.
(b) Does the point (16, -1) lie on this circle. Show why or why not

Answer 1

Step-by-step explanation:

x² + 12x + y² - 8y = 73

(x² + 12x + 36) + (y² - 8y + 16) = 73 + 36 + 16

(x + 6)² + (y - 4)² = 125.

Hence the coordinates of the center is (-6, 4).

Since (16 + 6)² + (-1 - 4)² = 22² + (-5)² = 509 and 509 is not equal to 125, (16, -1) does not lie on the circle.

Answer 2

A circle is a curve sketched out by a point moving in a plane. The point (16, -1) does not lie on this circle, as can be seen in the image below.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

A.) Given the equation of the circle is x²+ 12x + y² - 8y = 73, which can be written in the standard form as,

(x+6)²+(y-4)²=125

Hence, the coordinates of the centre of the circle are (-6,4).

B.) The point (16, -1) does not lie on this circle, as can be seen in the image below.

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