Question

2. Find the equation of the circle which touches the x-axis at a distance of 3 units from
the origin and makes an intercept of length 6 units on the y-axis.​

Answer 1

Answer:

Step-by-step explanation:

let equation of circle is ----

x^2+y^2+2gx+2fy+c=0========(2)

a/c to question,

circle touch x-axis at x=3

hence,

(3)^2+0+2(3)g+0+c=0

9+6g+c=0 -------------(1)

also we know circle touch x-axis then

g^2=c

put this above equation ,

9+6g+g^2=0

(g+3)^2=0

g=-3

again ,

put this equation (1)

9-18+c=0

c=9

a/c to question ,

y-intersept =6 unit

2√(f^2-c)=6

√(f^2-9)=3

aquaring both side

f=+_3√2

now put all constant in equation (2)

then ,

x^2+y^2-6x+(+_6√2)y +9=0