If the line x+2by+7=0 is a diameter of the circle x^2+y^2-4x+8y-13=0, then b=?

Question

Options: 

A- 3/9 

B- 8/9

C- -9

D- 9/8

Answer 1

Good morning,

 

This is how I solved the problem. If the line is a diameter of the circle, then it must go through the center of the circle.

 

If we plug in that point in the equation of the line, we can solve for b

 

To find the center, we put the equation of the circle in standard form.

 

First group terms with x together, terms with y together and move the 13 over to the right side.

 

(x² -4x) + (y² + 8y) = 13

 

Now complete the square

 

(x - 2)² + (y + 4)² =33

 

If you need help with completing the square you can google "completing the square Khan Academy video"

 

Now using the standard equation we can easily see that (2, -4) is the center

 

Plug in 2 for x and -4 for y using the linear equation

 

2 + 2b(-4) + 7 =0

 

-8b = -9

 

b=9/8

 

Answer D