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x^2+y=5, x^2+y^2=7

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

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(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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directrix (x+3)²=−20(y−1)

Solution

y=6

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Parabola Directrix

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

Rewrite (x+3)²=−20(y−1) in the standard form: 4(−5)(y−1)=(x−(−3))²

(h, k)=(−3, 1), p=−5

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance −p from the center (−3, 1) y-coordinate

y=1−p

y=1−(−5)

Refine

y=6

Non Linear Simultaneous Equations Examples

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

x^2+y=5, x^2+y^2=7

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