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lisov135 [29]
2 years ago
11

Write the equation of the circle with center (-4, 8) and passes through the point (-2, -1)

Mathematics
1 answer:
anzhelika [568]2 years ago
8 0

Answer:

(x+4)^2+(y-8)^2=85

Step-by-step explanation:

The standard equation for a circle is given by:

(x-h)^2+(y-k)^2=r^2

Where (h, k) is the center and r is the radius.

We know that the center is (-4, 8). So, substitute -4 for h and 8 for k:

(x-(-4))^2+(y-8)^2=r^2\\

Simplify:

(x+4)^2+(y-8)^2=r^2

Now, we will need to find r.

We know that it passes through the point (-2, -1). So, we can substitute -2 for x and -1 for y and solve for r. So:

(-2+4)^2+(-1-8)^2=r^2

Evaluate:

(2)^2+(-9)^2=r^2

Square:

4+81=r^2

Add:

r^2=85

So, r squared is 85.

We don’t actually have to solve for r itself, since we will have to square it anyways.

So, we have:

(x+4)^2+(y-8)^2=r^2

Substituting 85 for r squared, we get:

(x+4)^2+(y-8)^2=85

And we have our equation.

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