Find the equation of the circle

Step-by-step explanation:

Let's say the coordinates of Q are (h, k).

The slope of PQ is perpendicular to the tangent line.

(k − 2) / (h − 2) = -⅓

3(k − 2) = -(h − 2)

3(k − 2) = 2 − h

Solving for h:

h = 2 − 3(k − 2)

h = 2 − 3k + 6

h = 8 − 3k

(2, 2) is a point on the circle, so:

(2 − h)² + (2 − k)² = r²

Substituting:

9 (k − 2)² + (2 − k)² = r²

10 (k − 2)² = r²

The equation of the circle is:

(x − 8 + 3k)² + (y − k)² = 10 (k − 2)²

Without more information, there are an infinite number of possible solutions.  For example, if k = 1, the equation of the circle is:

(x − 5)² + (y − 1)² = 10

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

lol

step-by-step explanation: