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The equation of a circle is x2 + y2 − 4x + 6y + 4 = 0. On the grid provided below, draw the circle.
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Step-by-step solution
5 stepsTo draw the circle, we first need to find its center and radius from the given equation. We will convert the general form of the equation to the standard form by completing the square.
The given equation is:
Group the terms and terms, and move the constant to the right side of the equation.
Complete the square for the terms.
Take half of the coefficient of (which is ), square it (), and add it to both sides.
Complete the square for the terms.
Take half of the coefficient of (which is 6), square it (), and add it to both sides.
Rewrite the expressions in parentheses as squared terms and simplify the right side.
Identify the center and radius .
Comparing this to the standard form :
The center is .
The radius squared is 9, so the radius .To draw the circle on a grid, you would:
- Locate the center point at .
- From the center, measure out 3 units in all directions (up, down, left, right) to mark points on the circle.
- Draw a smooth curve connecting these points to form the circle.
The center of the circle is and the radius is .
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