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.

Options

A. `x^(2)+y^(2)-ax=0`
B. `x^(2)+y^(2)=1//a^(2)`
C. `y^(2)=4ax`
D. `x^(2)+y^(2)-ax+a^(2)=0`

Answer

B

Explanation

Since, `y=mx+c` is tangent to
`x^(2)+y^(2)=a^(2), ` if
`x+pmasqrt(1+m^(2))`
`thereforey=-(lx)/(m)+1/m` is tangent ot
`x^(2)+y^(2)=a^(2),`
If `1/m=pma/msqrt(l^(2)+m^(2))`
`impliesl^(2)+m^(2)=1//a^(2)`
Hence, locus of the point (l, m) is
`x^(2)+y^(2)=(1)/(a^(2)).`