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If there exists exactly one point of the line 3x+4y+25=0from which perpendicular tangesnt can be brawn to ellipse (x^(2))/(a^(2))+y^(2)=1(agt1),

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Solution :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))`


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