find-the-points-on-hyperbola-x-2-y-2-2-closest-to-point-0-1-

Question Number 97115 by bobhans last updated on 06/Jun/20

find the points on hyperbola x^{2} - y^{2} = 2

closest to point (0, 1)

Answered by mr W last updated on 06/Jun/20

x^{2} + {(y - 1)}^{2} = d^{2}

y^{2} + 2 + {(y - 1)}^{2} = d^{2}

2 y^{2} - 2 y + 3 - d^{2} = 0

Δ = {(- 2)}^{2} - 4 \times 2 \times (3 - d^{2}) = 0

2 d^{2} = 5

\Rightarrow d = \frac{\sqrt{10}}{2}

y = \frac{2}{2 \times 2} = \frac{1}{2}

x = \pm \sqrt{{(\frac{1}{2})}^{2} + 2} = \pm \frac{3}{2}

p o i n t s o n c u r v e :

(\pm \frac{3}{2}, \frac{1}{2})

Commented by bobhans last updated on 06/Jun/20

at point (\pm \frac{3}{2}, \frac{1}{2}) ?

Commented by bobhans last updated on 06/Jun/20

oo yes .

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