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On which curve does the perpendicular ta...

On which curve does the perpendicular tangents drawn to the hyperbola `(x^(2))/(25)-(y^(2))/(16)=1` intersect?

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The locus of the point of intersection of prependicular tangents to `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` is the director circle given by
`x^(2)+y^(2)=a^(2)-b^(2)`
Hence, the perpendicular tangents drawn to
`(x^(2))/(25)-(y^(2))/(16)=1`
intersect on the curve
`x^(2)+y^(2)=25-16=9`
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