First slide

Hyperbola in conic sections

Question

$Let P N be the ordinate of a point P on the hyperbola \frac{x^{2}}{(97)^{2}} - \frac{y^{2}}{(79)^{2}} = 1 and the tangent at$ $P meets the transverse axis in T, O is the origin. Then [\frac{O N . O T}{2020}] is equal to... (where$ [.] denotes Greatest integer function)

Moderate

Solution

$Given hyperbola is \frac{x^{2}}{(97)^{2}} - \frac{y^{2}}{(79)^{2}} = 1$
$Let P T be the equation of the tangent at ' P^{'} cuts the transverse axis at ' T^{'}$
$O N . O T = 97 \sec θ .97 \cos θ = 97^{2}$
$∴ [\frac{O N . O T}{2020}] = [\frac{97^{2}}{2020}]$
$= [\frac{9409}{2020}] = [4.657] = 4$

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