Find an equation of the tangent line at each of the four (4) of points on the curve (x 2 +y 2 −4x) 2 = 2(x 2 +y 2 ) where x = 1. this curve, whose general equation is given by (x 2 + y 2 − ax) 2 = b 2 (x 2 + y 2 ), for constants a and b, is an example of a lima¸con of pascal, named after french philosopher blaise pascal’s father, etienne ´ pascal, who first described it in 1650.

Step-by-step explanation:

To write an equation of the tangent lines, we need to know the locations of the tangent points, and the slope of the curve at those locations. To find the slope of the curve, we can implicitly differentiate and solve for dy/dx at x=1.

The derivative with respect to x of the given equation is ...

__

The points of tangency are the solutions to the given equation when x=1. Substituting z=y^2, that equation becomes ...

Solutions are z=7 or z=1, so ...

__

Putting these point values into the equation for the slope, we find ...

Then the tangent lines have equations ...

These are shown in the attached graph.

answer:

sometimes

*i think

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)