Which of the following is the equation for a circle with center (5, -1) and radius of 4?

Question

Which of the following is the equation for a circle with center (5, -1) and radius of 4?

(x + 5)2 + (y - 1)2 = 16

(x + 5)2 + (y - 1)2 = 4

(x - 5)2 = (y + 1)2 = 4

(x - 5)2 + (y + 1)2 = 16

Answer 1

It's the last one
(x - 5)2 + (y + 1)2 = 16

Answer 2

If you have a curve with equation y = f(x) and you moved the curve 'a' units to the right, the x co-ordinate of every point on the curve increases by 'a', right ? So, the new x co-ordinates won't satisfy y = f(x) any more ! To satisfy the equation, you will need to subtract 'a' from the x co-ordinate of each point. That is, the new equation the shifted curve will satisfy is y = f(x - a). This means that all occurrences of 'x' in the equation have to be replaced by 'x-a'. Similarly, if you shifted the curve 'b' units up, the y co-ordinate of each point will increase by 'b' and you will need to subtract 'b' from all co-ordinates to satisfy the equation. So, if a curve, y = f(x), is shifted by 'a' along the x axis and 'b' along the y axis, the new equation will be y - b = f(x - a) !!!!

In your case, the equation of a circle with center at (0,0) and radius 4 is (x)2 + (y)2 = 16. If the center goes to (5, -1), you have shifted it 5 units on the x axis and -1 units on the y axis.

So, the new equation will be: (x - 5)2 + (y + 1)2 = 16, the last one on your list !!

Answer 3

Equation of circle centre (a,b) and radius r is:
(x - a)² + (y - b)² = r²
In this case, a = 5 , b = - 1 and r = 4:-
(x - 5)² + (y + 1)² = 16

Answer 4

(x-5)^2 + (y+1)^2=16

Answer 5

I believe that it is the last one. The number at the end of the equation (i.e. the 4 or the 16) is supposed to be the square of the radius. That narrows it down to the first or the last one. Then you plug the X and Y into its respective places in the equation below, and simplify. Therefore, it is the last one

Answer: The last option.

equation is (x-h)^2 + (y-k)^2 = r^2

Answer 6

(x - 5)2 + (y + a million)2 = sixteen the effortless formulation is x^2+y^2=r^2 to pass it to incercept a element subtract the values from the relative x-,y- expression an identical way you do for a linear equation and the radius is squared additionally g'success and have relaxing

Answer 7

Remember that (x-h)^2 + (y-k)^2 = r^2 always describes the circle with center (h,k) and radius r. You chould be able to figure it out from there.

Answer 8

In your third choice, the first "=" should be a "plus".
The 4th choice is the correct answer. Just draw one out and try a few points.