If x^2 + y^2 - 2x - 4y = 20 , then an equation of the tangent line at (1, 7) is?... 3x - 4y + 30 = 0 ???

Question

I'm never sure when it comes to this level of math.

Answer 1

The equation you gave is the equation of a circle of radius 5 centered at the point (1,2). Here's how to see that:

First group the x terms and the y terms:

x^2 - 2x + y^2 - 4y = 20

Now add two constants on the left side to make two perfect square trinomials (completing the square). The constants are 1 and 4, so you have to add 5 to the right side to balance it.

x^2 - 2x + 1 + y^2 -4y + 4 = 25

Now rewrite the left side with the perfect squares expressed in factored form:

(x - 1)^2 + (y - 2)^2 = 25

Now you can see from the equation that the center is at (1,2) and the radius is 5.

The tangent line at (1,7) will be horizontal because the tangent to a circle is always perpendicular to the radius and the radius between (1,2) and (1,7) is vertical.

Thus the equation for the tangent line is simply y = 7.

Answer 2

i do no longer comprehend if the previous answer grow to be fairly a wild guess, besides the fact that it grow to be the main suitable suited one. First, you should discover the midsection of the circle by way of polishing off the sq. for x and y. You get: (x-one million)^2 + (y-2)^2 = 25 the midsection is at (one million,2). The tangent line at (-3,-one million) is the line perpendicular to the radial line connecting the midsection (one million,2) to (-3,-one million). So discover the slope of the radial line: m=(-one million-2) / (-3-one million) = 3/4 The slope of the tangent line ought to then be: m= - 4/3 Use this in y=mx+b: y= -(4/3)x + b to come across b, plug in one element you have for the tangent line: (-3,-one million). This yields b=-5. So, the equation of the tangent line is: y = -(4/3)x - 5 Written in regular type, you get: 4x +3y +15=0 hence the respond is f. desire this permits.

Answer 3

Both answers above are incorrect

3x - 4y - 20 = 0

Answer 4

X^2+y^2-2x-4y=20
2x+2y(dy/dx)-2-4(dy/dx)=0
2y(dy/dx)-4(dy/dx)=-2x+2
(dy/dx)(2y-4)=-2x+2
dy/dx=(-2x+2)/(2y-4)
Plugging in 1 and 7 to the dy/dx equation you get 0
y-7=0(x-1)
y=7

Answer 5

yes

Answer 6

???????????????????

sorry

tried it
came up with some strage answer