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 Bowers Kirk. in the United States
Feb 26,2025
Solución de inteligencia artificial de Upstudy
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The standard form of the circle's equation is \( (x - 8)^2 + (y - 6)^2 = 1 \).
Solución
The standard form of a circle’s equation with center (h, k) and radius r is given by:
(x – h)² + (y – k)² = r²
Plugging in h = 8, k = 6, and r = 1, we have:
(x – 8)² + (y – 6)² = 1
This is the standard form of the equation for the given circle.
To graph the circle:
1. Plot the center at (8, 6).
2. Since the radius is 1, mark points 1 unit above, below, left, and right of the center.
3. Draw a smooth curve connecting these points to form the circle.
The final answer in standard form is:
(x – 8)² + (y – 6)² = 1
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Simplifique esta solución The Deep Dive
The standard form of the equation of the circle with radius \( r = 1 \) and center \( (h, k) = (8, 6) \) is given by: \[ (x - 8)^2 + (y - 6)^2 = 1 \] The general form of the equation can be derived by expanding the standard form. This leads to: \[ x^2 - 16x + 64 + y^2 - 12y + 36 = 1 \] Simplifying this gives: \[ x^2 + y^2 - 16x - 12y + 99 = 0 \] To graph the circle, you would plot the center at the point (8, 6) and then draw a circle with a radius of 1, which extends one unit in all directions from the center. It will touch the points (9, 6), (7, 6), (8, 7), and (8, 5). Happy graphing!
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