Pregunta
\( 1 \leftarrow \begin{array}{l}\text { Write the standard form of the equation and the general form of the equation of the circle with } \\ \text { radius } r \text { and center }(h, k) \text {. Then graph the circle. } \\ r=1 ; \quad(h, k)=(8,6)\end{array} \) The standard form of the equation of this circle is (Type your answer in standard form.)
Ask by Lyons Daniels. in the United States
Feb 26,2025
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The standard form of the equation is \((x - 8)^2 + (y - 6)^2 = 1\).
Solución
The standard form of the equation of a circle with center (h, k) and radius r is:
(x – h)² + (y – k)² = r²
For h = 8, k = 6, and r = 1, it becomes:
(x – 8)² + (y – 6)² = 1
To graph the circle:
1. Plot the center at (8, 6).
2. Since the radius is 1, mark points 1 unit away from (8, 6) in all directions (up, down, left, and right).
3. Draw a smooth curve connecting these points, forming the circle.
Thus, the standard form of the equation is:
(x – 8)² + (y – 6)² = 1
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Simplifique esta solución Beyond the Answer
The standard form of the equation of the circle with radius \( r = 1 \) and center \( (h, k) = (8, 6) \) is given by: \[ (x - 8)^2 + (y - 6)^2 = 1 \] To express this in general form, we can expand the equation: \[ (x - 8)^2 + (y - 6)^2 - 1 = 0 \] Expanding gives: \[ x^2 - 16x + 64 + y^2 - 12y + 36 - 1 = 0 \] Which simplifies to: \[ x^2 + y^2 - 16x - 12y + 99 = 0 \] Now you can plot the circle simply! Center your graph at the point (8, 6) and draw a circle with a radius of 1 unit. Voilà!
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