Find the y intercept of the circle with center (-1,2) and with radius 1.

Answer 1

The conic section equation for the circle with center (h,k) and radius r:

(x-h)²+(y-k)² = r²

For (-1,2) and r=1:

(x+1)²+(y-2)² = 1

The y-intercept is when x = 0.

1 + (y-2)²=1

(y-2)² = 0

y-2 = 0

y = 2

Answer 2

Given the center and radius, we can put find an equation for this circle from the general form:

(x-x_c)² + (y-y_c)² = r²

Where (x_c,y_c) is the coordinate of the circle's center. Thus, the circle described is written as:

(x+1)²+(y-2)² = 1

The y-intercept is found when x = 0. Substituting this into the equation gives:

1 + (y-2)² = 1

(y-2)² = 0

y-2 = 0

y = 2

Answer 3

If you graph the circle, it should be evident that the circle will just touch the y-axis 1 unit to the right of its center, at (-1 , 1).