If x2 + y2 - 2x - 4y = 20 , then an equation of the tangent line at (4, -2) is?

Question

a. 3x + 4y - 36 = 0

b. 4x + 3y - 35 = 0

c. 3x - 4y + 30 = 0

d. 4x - 3y - 23 = 0

e. 3x + 4y + 14 = 0

f. 4x + 3y + 15 = 0

g. 3x - 4y - 20 = 0

h. 4x - 3y + 27 = 0

i. none of these




This is not my homework
I'm not even in enrolled in a Calculus class.

I'm tring to teach myself this summer and pass the class next year.

Answer 1

Use implicit differentiation to take the derivative. You get:

2x + 2y(dy/dx) – 2 – 4(dy/dx) = 0

Then solve to get dy/dx by itself.

(dy/dx)(2y-4) = 2 – 2x

(dy/dx) = (2 – 2x)/(2y – 4) = (1 – x)/(y – 2)

Then plug in the given point:

(1 – 4)/(-2 – 2) = ¾

¾ is the slope taken anywhere.

You then have to use point slope form.

y + 2 = ¾ (x - 4)
y = ¾x – 5
multiply the entire thing by 4
4y = 3x – 20
rearrange the equation
4y – 3x + 20 = 0
then multiply by (-) to match the answer.
-4y + 3x – 20 = 0

so your answer is G.

Answer 2

I don't know if the previous answer was truly a wild guess, but it was the correct one. First, you must find the center of the circle by completing the square for x and y. You get: (x-1)^2 + (y-2)^2 = 25 The center is at (1,2). The tangent line at (-3,-1) is the line perpendicular to the radial line connecting the center (1,2) to (-3,-1). So find the slope of the radial line: m=(-1-2) / (-3-1) = 3/4 The slope of the tangent line must then be: m= - 4/3 Use this in y=mx+b: y= -(4/3)x + b To find b, plug in one point you have for the tangent line: (-3,-1). This yields b=-5. So, the equation of the tangent line is: y = -(4/3)x - 5 Written in standard form, you get: 4x +3y +15=0 Thus the answer is f. Hope this helps.

Answer 3

ok well I think maybe that...
2x+2y-2x-4y=20
2x-2x+2y-4y=20
0-2y=20
-2y=20
y=20/-2
y=-10
I think. I'm only 13 but we do algebra alot and I think that's how it goes. What you always do is collect like terms. For example, if you had 3x+4y-3x-4y, you put all the xs and ys with their own kind of "family" so it turns out like this: 3x-3x+4y-4y
Do u understand now?
I don't understand the tangeant line thingy but yeah. So I'm guessing that...
a. 3x+4y-36=0
3x+4y=0+36 (If you're going to the other side of an = sign, you always convert!)
3x+4y=36
and i don't understand the rest...
Hopefully this has helped you a little :)
Good Luck!
-Stampy x x x

Answer 4

x^2 + y^2 - 2x - 4y = 20
2xdx + 2ydy - 2dx - 4dy = 0
(2x - 2)dx + (2y - 4)dy = 0
dy/dx = - (x - 1)/(y - 2) =
- (4 - 1)/(- 2 - 2) = 3/4 @ (4,-2)

y + 2 = (3/4)(x - 4)
4y + 8 = 3x - 12
3x - 4y - 20 = 0
y = (3/4)x - 5

Answer 5

x2 + y2 - 2x - 4y = 20
Differentiate with respect to x,
2x+2yy'-2-4y' = 0
8-4y'-2-4y' = 0
y' = 3/4

3x-4y = c
12+8 = 20 = c

3x-4y-20 = 0

Therefore g is the answer.