derivada implícita (dy)/(dx), (x-y)^2=x+y-1

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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

implicit derivative tangent volume laplace fourier

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Steps Examples

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foci (x−1)²9 +y²5 =100

Solution

(21, 0), (−19, 0)

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Solution steps

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Ellipse Foci

For an ellipse with major axis parallel to the x-axis, the Foci (focus points) are defined as (h+c, k), (h−c, k),
where c=√a²−b² is the distance from the center (h, k) to a focus

(h+c, k), (h−c, k)

Calculate ellipse properties

(x−1)²9 +y²5 =100: Ellipse with center (h, k)=(1, 0), a=30, b=10√5

(1+c, 0), (1−c, 0)

Compute c:

c=√30²−(10√5)²: 20

(1+20, 0), (1−20, 0)

Refine

(21, 0), (−19, 0)

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