foci (y-3)^2=8(x-5)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for expand factor rationalize

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foci (y−3)²=8(x−5)

Solution

(7, 3)

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Parabola Focus

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (the directrix)

Parabola standard equation

4p(x−h)=(y−k)² is the standard equation for a right-left facing parabola with vertex at (h, k),
and a focal length |p|

Rewrite (y−3)²=8(x−5) in the standard form: 4· 2(x−5)=(y−3)²

(h, k)=(5, 3), p=2

Parabola is symmetric around the x-axis and so the focus lies a distance p from the center (5, 3) along the x-axis

(5+p, 3)

=(5+2, 3)

Refine

(7, 3)

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