X^2-8x+y^2=9 what is the radius
1 answer:
Answer:
5
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
To express
x² - 8x + y² = 9 in this form complete the square on the x- terms
x² + 2(- 4) x + (- 4)² + y² = 9 + (- 4)²
(x - 4)² + y² = 9 + 16 = 25 ← in standard form
with centre = (4, 0) and r = = 5
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"determine the location" or namely, is it inside the circle, outside the circle, or right ON the circle?
well, we know the center is at (1,-5) and it has a radius of 5, so the distance from the center to any point on the circle will just be 5, now if (4,-1) is less than that away, is inside, if more than that is outiside and if it's exactly 5 is right ON the circle.
well, we can check by simply getting the distance from the center to the point (4,-1).