# How do you find the equation of tangent line to the curve #y= sqrt(3+x^2)# that is parallel to the line x-2y=1?

There are two possible equations:

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First, find the derivative of the function.

We can now use the slope and the points to find the equation of each tangent.

Hopefully this helps!

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To find the equation of the tangent line to the curve y = sqrt(3 + x^2) that is parallel to the line x - 2y = 1, we need to follow these steps:

- Differentiate the equation of the curve y = sqrt(3 + x^2) with respect to x to find the derivative dy/dx.
- Set the derivative dy/dx equal to the slope of the given line x - 2y = 1, which is 1/2.
- Solve the resulting equation for x to find the x-coordinate(s) of the point(s) where the tangent line is parallel to the given line.
- Substitute the x-coordinate(s) obtained in step 3 into the original equation y = sqrt(3 + x^2) to find the corresponding y-coordinate(s).
- Use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the tangent line and m is the slope, to write the equation of the tangent line using the coordinates found in step 4.

By following these steps, you will obtain the equation of the tangent line to the curve y = sqrt(3 + x^2) that is parallel to the line x - 2y = 1.

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