If lx + my -1 = 0 touches the circle x^2...

If lx + my -1 = 0 touches the circle `x^2 + y^2 = a^2` then the point (l,m) lies on the circle

Verified by Experts

C(0,0),r=a
`d=|(0+0-1)/sqrt(l^2+m^2)|=a`
`1/(l^2+m^2)=a^2`
`l^2+m^2=1/a^2`
`l^2+m^2=a^(-2)`
`x^2+y^2=a^(-2)`
option C is correct.

Similar Questions

Explore conceptually related problems

If lx + my = 1 touches the circle x^2 + y^2 = a^2 , prove that the point (l, m) lies on the circle x^2 + y^2 = a^(-2)

If lx+my=1 touches the circle x^(2)+y^(2)=a^(2) , prove that the point (l,m) lies on the circle x^(2)+y^(2)=a^(-2)

If the line lx + my = 1 is a tangent to the circle x^(2) + y^(2) = a^(2) , then the point (l,m) lies on a circle.

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.

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

If the line 2x-y+1=0 touches the circle at the point (2,5) and the centre of the circle lies in the line x+y-9=0. Find the equation of the circle.