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A tangent to a hyperbola x^2/a^2 - y^2/b...

A tangent to a hyperbola `x^2/a^2 - y^2/b^2 = 1` intercepts a length of unity from each of the coordinate axes, then the point `(a, b)` lies on rectangular hyperbola

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let the eqn of hyperbola be
`H : x^2/a^2 -y^2/b^2 = 1`
let the point on it be `(a sec theta, b tan theta)`
the equation of tangent will be
`bxsec theta - ay tan theta = ab`
putting y=0
`bxsec theta = ab `
`x= a cos theta = 1`
...
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