Question

If the line `l x+m y-1=0` touches the circle `x^2+y^2=a^2` , then prove that `(l , m)` lies on a circle.

Answer 1

True
Given circle is `x^(2)+y^(2)=a^(2)`
`therefore` Radius of circle=a and centre =(0,0)

`therefore` Distance from point (l,m) and centre is `sqrt((0-e)^(2)+(0-m)^(2))`=a
`rArr l^(2)+m^(2)=a^(2)`
So, l,m lie on the circle.