Equation of Circle: Centre (2,-4), y-intercept 1

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To find the equation of a circle with center (2,-4) and a y-intercept of 1, the radius must be determined using the y-intercept point (0,1). The standard equation of a circle is (x-a)² + (y-b)² = r², where (a,b) is the center and r is the radius. The discussion also briefly touches on another circle centered at (5,4) that intersects the x-axis, but the focus remains on calculating the first circle's equation. The process emphasizes the simplicity of using given points to derive the radius and complete the equation. Understanding these concepts is crucial for solving similar problems effectively.
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Homework Statement



find the equation of a circle with centre of (2,-4) and y-intercept 1

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The Attempt at a Solution

 
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The equation of a circle of radius r centered at the point (a,b) is given by (x-a)2+(y-b)2=r2. Since you already are given the point (a,b), all you need to find is the radius of the circle. Can you use the information that a y-intercept is (0,1) to find the radius?
 
n!kofeyn said:
The equation of a circle of radius r centered at the point (a,b) is given by (x-a)2+(y-b)2=r2. Since you already are given the point (a,b), all you need to find is the radius of the circle. Can you use the information that a y-intercept is (0,1) to find the radius?

Thank you so much I didn't know it was that simple xD ok then can I ask something else:

A circle with a centre (5,4) intersects the x-axis 3 units from the origin. Find the possible equations of the circle.

Never mind i got it :D
 
Last edited:
Ok, cool!
 

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