Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). an equation of the tangent line to the lemniscate at the given point is

The equation of the tangent line to the curve is expressed as

The formula for calculating the equation of a line in point-slope form is expressed as y-y0 = m(x-x0)

m is the slope

(x0, y0) is the point on the line

Given the equation

To get the required slope, we will need to differentiate the equation implicitly with respect to x as shown:

Substituting the coordinate point (-3, 1)

Write the expression in point slope form:

Hence the equation of the tangent line to the curve is expressed as

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Let , so that differentiating both sides wrt gives

If and , the above reduces to

This is the slope of the tangent line, which has equation

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step-by-step explanation:

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.