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Chapter 1: Problem 73

Write the standard form of the equation of the circle with the given characteristics. Center: (-1,2)\(;\) Solution point: (0,0)

Short Answer

Expert verified
The equation of the circle in standard form is \((x + 1)^2 + (y - 2)^2 = 5\).

Step by step solution

01

Find the Radius

Finding the radius requires using the distance formula to calculate the distance between the center point (-1, 2) and the solution point (0,0). The distance formula is: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Substituting the given coordinates, we get \(\sqrt{(0 - (-1))^2 + (0 - 2)^2}\), which simplifies to \(\sqrt{1+4} = \sqrt{5}\). Therefore, the radius \(r = \sqrt{5}\).
02

Write the Equation

Using the coordinates of the center (-1, 2) and the radius \(\sqrt{5}\) , we can substitute these values into the standard form of a circle equation \((x-h)^2 + (y-k)^2 = r^2\). This gives us: \((x - (-1))^2 + (y - 2)^2 = (\sqrt{5})^2\), which simplifies to \((x + 1)^2 + (y - 2)^2 = 5\). This is the standard form of the equation of the circle.

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