Question

A circle is tangent to both negative x axis and positive y axis and passes through the point (-4, 6). The sum of the radii of all such

posiible circles is​

Answer 1

Answer:

20

Step-by-step explanation:

A circle is tangent to both negative x axis and positive y axis and passes through the point (-4, 6). The sum of the radii of all such

Let say radius = r

as Circle is tangent to -x axis & y axis

so center point would be  ( - r , r)

As circle passes through point (-4 , 6)

so distance between center (-r , r)  & ( - 4 , 6)  would be equal to radius

=>  r² = ( -r -(-4))² + (r - 6)²

=> r² = r² + 16 - 8a + r² + 36 - 12a

=> r² - 20a + 52 = 0

=> r =  (20 ± √(400 - 208 )/2

r = 10 + 4√3  & 10 - 4√3

Sum of radius = 10 + 4√3 + 10 - 4√3 = 20