Google Classroom(x−h)2+(y−k)2=r2The formula relates the x - and y-coordinates of a point on a circle with a center at (h,k) to the radius r. Which of the following equations correctly gives y in terms of x,h,k, and r ?Choose 1 answer:(A) y=r−x+h+k(B) y=r−(x−h)2+k(C) y=±r2−(x−h)2+k(D) y0Show calculator
Q. Google Classroom(x−h)2+(y−k)2=r2The formula relates the x - and y-coordinates of a point on a circle with a center at (h,k) to the radius r. Which of the following equations correctly gives y in terms of x,h,k, and r ?Choose 1 answer:(A) y=r−x+h+k(B) y=r−(x−h)2+k(C) y=±r2−(x−h)2+k(D) y0Show calculator
Start Equation Circle: Start with the given equation of a circle.The equation of a circle with center (h,k) and radius r is given by:(x−h)2+(y−k)2=r2We need to solve this equation for y in terms of x, h, k, and r.
Isolate Term: Isolate the (y−k)2 term.To solve for y, we first need to isolate the (y−k)2 term on one side of the equation. We do this by subtracting (x−h)2 from both sides of the equation:(y−k)2=r2−(x−h)2
Take Square Root: Take the square root of both sides.To solve for y, we take the square root of both sides of the equation. Remember that taking the square root of both sides introduces a plus or minus (±) sign:y−k=±r2−(x−h)2
Solve for y: Solve for y.Finally, we add k to both sides of the equation to solve for y:y=k±r2−(x−h)2
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