What is the tangent line of x^2 + y^2 = 36 at the point: (X=1 and Y=square root of 35?

Answer 1

y=sqrt(36-x^2)
y'=1/2(36-x^2)^{-1/2}(-2x)
=-x/(36-x^2)^{1/2}
x=1,
y'= -1/sqrt(35)
so the equation of the tangent line is:
y-sqrt(35)=-1/sqrt(35)(x-1)

Answer 2

Solve the equation for y, making sure that you use the right sign for the square root (depending on whether the problem refers to the positive or negative square root of 35).

Now you have y as a function of x. Take the derivative (i.e., determine dy/dx). This is the slope of the tangent line.

Now you need to write the equation of a line with a known slope that passes through the point (1, sqrt(35)), and you'll be done.

Answer 3

you like the spinoff to get the slope on the factor (4,2) The spinoff of y =sqrt(x) is dy/dx = a million/2 x^(-a million/2) this is the slope of the tangent line at any factor So, at x=4, the slope is a million/2 4^(-a million/2) =a million/4 Now you have the slope (a million/4) and a factor (4,2), so making use of the factor slope formula, you need to have the skill to get the equation of the tangent line, especially, (2-y) = a million/4 (4-x) is your equation. you may improve & simplify this to get 4y - x = 4 (answer)

Answer 4

To solve this problem, we need to find the slope of the line on the curve at (3, sq rt 35)
The slope of our tangent line is the same as the instantaneous slope of the line at this point.
Find this slope by taking the first derivative of the function. (It is a circle if graphs help you to see it, with its center at (0,0) and a radius of 6)

The easiest way to find the first derivative is to do it by implicit differentiation:

d(x^2)/dx + d( y^2)/dx = d(36)/dx

We get 2x(dx/dx) + 2y(dy/dx) = 0
dx/dx = 1

2x + 2y(dy/dx) = 0

Solving for dy/dx, we get
dy/dx = -x/y

now substitute the point you were given into this derivative and you will have the slope of the line you are looking for.
Use this same point and the point slope formula for a straight line to write the equation you need.

Answer 5

to find the tangent line of an equation, you need to find the derivative of that equation. in this case, the equation can be re-arranged into y^2 = 36 - x^2. to simplify, that equation becomes: y = root of (36 - x^2). then, we need to find the derivative of y.

dy/dx (root of (36 - x^2)) = (-2x) (0.5 (36 - x^2)^(-0.5))

to be clear, dy/dx ((36 - x^2)^(0.5)) = (-2x) (0.5 ((36 - x^2)^(0.5)))