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Gnesinka [82]
3 years ago
5

Find an equation of the circle and sketch it if it has: Center on y=4, tangent x-axis at (–2, 0)

Mathematics
1 answer:
Digiron [165]3 years ago
4 0

Answer:

(x+2)^2+(y-4)^2=16

OK, lets start by drawing a basic graph (the first one) so we can visualize.

We already know that the y coordinate of the circle's center is 4.

We know that the circle is tangent to the X axis at (-2,0)

That means the x coordinate of the center has to be -2, as the tangent is a point on the edge of the circle that touches a line at exactly one point.

The radius is the distance from the center of the circle to its edge. We know the center's location now, it is (-2, 4) and a point on the edge of the circle (the tangent point) which is (-2,0). so the distance between the points is 4 which is the radius (you can use the distance formula, but it's quite oblivious.)

We can imagine the circle should look like this (the second one):

Now we can piece together an equation

The equation of a circle is (x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius. When we put the numbers in: we get (x-(-2))^2+(y-(4))^2=4^2 which can be simplified into (x+2)^2+(y-4)^2=16 which is the answer.

Step-by-step explanation:

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