How to find the equation of the normal to the curve?

Find the equation of the normal to the curve $y= \\frac{x-2}{1+2x}$ (1) at the point where the curve cuts the $x$-axis . Find the coordinates of the point where this normal cuts the curve again . I found The equation of the normal –

What is the best way to find the slope of a curve?

Currently, we tend to don’t continually y-intercept, therefore a rather totally different variety of line equations is commonly useful: ), wherever m is our slope, and x 1 and y 1 are the coordinates of some extent. Example 1: Find the slope of the curve y = (1 + x)sin x at x = π/4.

What is the difference between tangent and normal in calculus?

In the application of derivatives, tangents and normals are important concepts. Each normal line is perpendicular to the tangent line drawn at the point where the normal meets the curve. So the slope of each normal line is the opposite reciprocal of the slope of the corresponding tangent line, which can be derived by the derivative.

How do you find the normal line equation for perpendicular lines?

Perpendicular lines slopes are negative reciprocal to each other. So – 1/3 slope of normal line to the curve at (1, 4). To find the normal line equation, substitute the values of m = (-1/3) and (x, y) = (1, 4). in the slope intercept form of an equation y = mx + b.

What is the slope of the tangent line to the curve?

Substitute the value x = 1 in above equation. This is the slope of tangent line to the curve at (1, 4). Tangent line and normal line are perpendicular. Perpendicular lines slopes are negative reciprocal to each other. So – 1/3 slope of normal line to the curve at (1, 4).

What does parallel to the x axis mean?

Parallel to the x axis means an equation y = constant. So the coefficient on x must be zero: Similarly parallel to the y axis means 2s +r = 0 which should just swap x and y due to the symmetry of the problem. So the other points are Check.

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