Locus of point of intersecrtion fo perpendicular tangents is director circle.
If there axists exactly one such point on the line 3x+4y+25=0, then line must touch the dierector circle whose equation is `x^(2)+y^(2)=a^(2)=1`
Distance of centre of the circle from the line is 5.
So, we must have
`25=a^(2)+1`
`rArr a^(2)=24 :. a =sqrt(24)`
`:.` Electricity `sqrt(1-(1)/(24))=sqrt((23)/(24))`