Question

Find the equation of the tangent at ( 0 , 2) to the circle with equation 
(x + 2)2 + (y + 1)2 = 13​

Answer 1

(-2 , -1) : center of circle

m = (2 - -1) / (0 - -2) = 3 / 2 : slope of line through the center and the point of tangency (0 , 2)

The line through the center and the point of tangency (0 , 2) is perpendicular to the tangent.

M = -2 / 3 : slope of tangent

y = -(2/3)x + 2 : equation of tangent given its slope and point (0 , 2).

Answer 2

answer

The given equation represents a circle centered at (2, -1) and radius equal to

√

13

. First locate the point (2, -1) on the graph and the next task is to measure a radius equal to

√

13

. For this draw a right triangle with sides 12 and 5 units. Then with radius equal to the hypotenuse draw the required circle using (2, -1) as the center using compass.