Equation of Tangent Line for Curve at (5,-3)

In summary, the conversation discusses finding the equation of the line tangent to a curve, represented as a circle with radius 3 and center (2,-3), at the point (5, -3). The derivative is solved to be dy/dx = ((-2x+4)/ (2y+6)), but when plugging in the point, the slope is found to be -6/0, which is undefined. The equation of a line with an undefined gradient is x=1, but since the curve is a circle, the equation of the tangent line is x=5.
  • #1
koolkris623
19
0
Find the equation of the line tangent to the curve at (5, -3)
(x-2)^2 + (y+3)^2 = 9

I solved the derivative to be dy/dx = ((-2x+4)/ (2y+6))

when i plugged in the points (5, -3) I got the slope as -6/0...How is this possible??
How can i find the equation of this curve if the slope is undefined??
 
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  • #2
If the gradient is undefined then, the tangent is vertical line e.g.x=1

btw: that curve, represents a circle with radius 3 and centre (2,-3) so if you are still confused about it, just make a sketch and see
 
Last edited:
  • #3
wait if its a circle then why isn't the equation x = 5?
 
  • #4
The equation is x=5, I just used x=1 as an example of what the equation of a line with an undefined gradient looks like
 

1. What is the equation for a tangent line to a curve?

The equation for a tangent line to a curve is y = mx + b, where m is the slope of the tangent line and b is the y-intercept.

2. How do you find the slope of a tangent line to a curve?

The slope of a tangent line to a curve can be found by taking the derivative of the equation for the curve at a specific point. This will give the slope of the curve at that point, which is also the slope of the tangent line.

3. Can a tangent line intersect a curve at more than one point?

No, a tangent line can only intersect a curve at one point. This is because a tangent line is defined as a line that touches a curve at only one point and has the same slope as the curve at that point.

4. What is the significance of a tangent line to a curve?

The tangent line to a curve is significant because it provides information about the slope of the curve at a specific point. This can be useful in determining the rate of change of a function, finding maximum and minimum points, and graphing the curve accurately.

5. Can a curve have multiple tangent lines at the same point?

No, a curve can only have one tangent line at a given point. This is because a tangent line represents the instantaneous slope of a curve at a point, and there can only be one slope at a specific point on a curve.

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