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Question Number 209125 by Spillover last updated on 02/Jul/24

Answered by mr W last updated on 03/Jul/24

Commented by mr W last updated on 05/Jul/24

AB=AF=a a+a cos θ=2p ⇒cos θ=((2p)/a)−1

$${AB}={AF}={a} \\ $$$${a}+{a}\:\mathrm{cos}\:\theta=\mathrm{2}{p} \\ $$$$\Rightarrow\mathrm{cos}\:\theta=\frac{\mathrm{2}{p}}{{a}}−\mathrm{1} \\ $$

Commented by Spillover last updated on 03/Jul/24

nice solution thank you

$${nice}\:{solution}\:{thank}\:{you} \\ $$

Commented by Spillover last updated on 03/Jul/24

Answered by Spillover last updated on 03/Jul/24

Commented by Spillover last updated on 04/Jul/24

thank you very for your clarification.

$${thank}\:{you}\:{very}\:{for}\:{your}\:{clarification}. \\ $$

Commented by mr W last updated on 03/Jul/24

but cos θ=−1+((2p)/a)

$${but}\:\mathrm{cos}\:\theta=−\mathrm{1}+\frac{\mathrm{2}{p}}{{a}} \\ $$

Commented by Spillover last updated on 03/Jul/24

why 2p? what is reason behind

$${why}\:\mathrm{2}{p}?\:{what}\:{is}\:{reason}\:{behind} \\ $$

Commented by mr W last updated on 03/Jul/24

distance from focus to vertex is p distance from focus to directrix is 2p see also my diagram above.

$${distance}\:{from}\:{focus}\:{to}\:{vertex}\:{is}\:{p} \\ $$$${distance}\:{from}\:{focus}\:{to}\:{directrix}\:{is}\:\mathrm{2}{p} \\ $$$${see}\:{also}\:{my}\:{diagram}\:{above}. \\ $$

Commented by mr W last updated on 03/Jul/24

Answered by Spillover last updated on 05/Jul/24

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