# How do you write an equation for a circle tangent to the line 5x + y = 3 at the point (2,-7) and the center is on the line x – 2y= 19?

##### 1 Answer

Please see the explanation. The equation is:

#### Explanation:

Write the equation of the tangent line in slope-intercept form so that we may observe its slope.

The slope

Because radius of the circle at point (2, -7) will be perpendicular to the tangent line, the slope of the radius is the negative reciprocal of the slope of the tangent line,

The center

Substitute equation [1] into equation [2]:

Substituting for x in equation [2]:

Substitute the center

#r = sqrt(26)