parity ((z-8)^2)/(z^2-64)

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

☐²

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∫

ddx

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

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foci (y−2)=3(x−5)²

Solution

(5, 2512 )

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Solution steps

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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(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 (y−2)=3(x−5)² in the standard form: 4· 112 (y−2)=(x−5)²

(h, k)=(5, 2), p=112

Parabola is symmetric around the y-axis and so the focus lies a distance p from the center (5, 2) along the y-axis

(5, 2+p)

=(5, 2+112 )

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(5, 2512 )

Description

The Limit Calculator is an essential online tool designed to compute limits of functions efficiently. Here's how to use it:

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Choose the approach to the limit (e.g., from the left, from the right, or two-sided).
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