Question

Find the equation of the circle which touches the lines `4x-3y+10=0a n d4x-3y-30=0` and whose centre lies on the line `2x+y=0.`

Answer 1

`4x-3y+10=0`
`4x-3y-30=0`
solving the line
`(2x+y=0)`and`(4x-2y+10=0)`
`x=-1,y=2`
Solving the line
`(4x-3y-3=0)`and`(2x+y=0)`
`x=3,y=-6`
Distance between parallel line=d
`|(10-(-30))/sqrt(16+9)|=d`
`d=|(10+30)/5|`
`d=8`
`r=4`
O is mid point of AB
`(x,y)=((3-1)/2,(2-6)/2)=(1,-2)`
A circle passes through center`(1,-2)`
`(x-1)^2+(y+2)^2=4^2`.