shortest-distance-from-6-0-to-x-2-y-2-16-0-

Question Number 201829 by 281981 last updated on 13/Dec/23

s h o r t e s t d i s t a n c e f r o m (- 6, 0) t o x^{2} - y^{2} + 16 = 0

Answered by esmaeil last updated on 13/Dec/23

d = \sqrt{{(x + 6)}^{2} + y^{2}} = \sqrt{\overset{2}{x} + 12 x + 36 + \overset{2}{x} + 16} =

Missing \left or extra \right

i f (x = - 3) \to d = s h o r t e s t = \sqrt{34}

Commented by 281981 last updated on 14/Dec/23

t n q s i r

Answered by mr W last updated on 13/Dec/23

{(x + 6)}^{2} + y^{2} = d^{2}

x^{2} - y^{2} + 16 = 0

x^{2} - d^{2} + {(x^{2} + 6)}^{2} + 16 = 0

2 x^{2} + 12 x + 52 - d^{2} = 0

Δ = 12^{2} - 4 \times 2 \times (52 - d^{2}) = 0

d^{2} = 34

\Rightarrow d = \sqrt{34}

Commented by 281981 last updated on 14/Dec/23

t n q s i r

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