which is the equation of a circle with center (0,1) and radius 2 units?

Question

a. x^2+y^2+2y=3
b. x^2+y^2+2y=1
c. x^2+y^2-2y=4
d. x^2+y^2-2y=3

Answer 1

Equation of circle with center(0,1)
and radius = 2

(x-0)^2 + (y-1)^2 = 2^2
x^2 + y^2 - 2y +1 = 4
x^2 + y^2 - 2y = 3 (answer d)

Answer 2

Circle centre (a,b) and radius r has equation:-
(x - a)² + (y - b)² = r²
In this case, a = 0, b = 1 and r = 2 so equation is:-
x² + (y - 1)² = 2²
x² + y² - 2y + 1 = 4
x² + y² - 2y = 3 which is answer d)

Answer 3

The equation of any circumference (not circle!) is this one:

x^2 + y^2- 2ax - 2by + a^2 + b^2 -r^2 = 0

where r is the radius, and the center is C(a,b)

So, just substitute

The equation of a circle is not this one, the distance between the points of circle and the center is not fixed distance, thats why you have to use a <

So, the equation of a circle whose radius is r and whose center is C(a,b) is this one

x^2 + y^2- 2ax - 2by + a^2 + b^2 -r^2 < 0

Take care

Ana

Answer 4

The answer is (d) as 0 = h and 1=k, and r =2

Using the equation (x-h)^2+(y-k)^2 = r2, we can substitute the values and rearrange to give x^2+y^2-2y=3

Answer 5

c