SOLUTION: How do i do question number 77 on 10.3
Write an equation of the line that is tangent to the circle at that point.
77) x2+ y2= 244; (-10, -12)
Please explain the steps..
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Question 193197: How do i do question number 77 on 10.3
Write an equation of the line that is tangent to the circle at that point.
77) x2+ y2= 244; (-10, -12)
Please explain the steps..
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the tangent line, we need the slope of the tangent line. To find that, we first need the first derivative of "y":
... Start with the given equation.
=\frac{d}{dx}(244))
... Derive both sides with respect to "x"
... Derive the left and right sides. Note: remember, y is a function of "x", so use the chain rule.
... Subtract 2x from both sides.
... Divide both sides by 2y.
... Reduce
So the slope of any tangent line at the point (x,y) (on the circle) is
Now just plug in the values and to find the tangent slope at (-10,-12):
... Reduce
So the slope of the tangent line is
Now let's find the equation of the line that has a slope of and goes through (-10, -12):
If you want to find the equation of line with a given a slope of which goes through the point (-10,-12), you can simply use the point-slope formula to find the equation:
---Point-Slope Formula---
where is the slope, and )
is the given point
So lets use the Point-Slope Formula to find the equation of the line
Plug in , , and (these values are given)
Rewrite as
Rewrite as
Distribute
Multiply and to get
Subtract 12 from both sides to isolate y
Combine like terms and to get
------------------------------------------------------------------------------------------------------------
Answer:
So the equation of the tangent line is
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Write an equation of the line that is tangent to the circle at that point.
77) x2+ y2= 244; (-10, -12)
Please explain the steps..
----------------
The slope, m, of a circle (and ellipse) at any point is -x/y (if you need to see proof of that, email me via the thank you note)
At (-10,-12), m = -5/6
-----------------
y+12 = -(5/6)*(x+10)
6y+72 = -5x - 50
5x+6y = -122
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