# Thread: tangents and normals

1. ## tangents and normals

find the equation of the tangent and normal of the curve y=x^2 + 5 where x = 0
this is simple and i have no problem finding the gradient and equation of the tangent, but the gradient of the normal is not defined (divided by zero) and i do not know what this means when introduced into the equation y-y1 = m (x - x1)

2. Originally Posted by furor celtica
find the equation of the tangent and normal of the curve y=x^2 + 5 where x = 0
this is simple and i have no problem finding the gradient and equation of the tangent, but the gradient of the normal is not defined (divided by zero) and i do not know what this means when introduced into the equation y-y1 = m (x - x1)

Undefined means that it has no slope i.e. it is a vertical line. the equation to the normal line is x=0,

3. so a horizontal line has gradient 0 and a vertical line has gradient undefined?

4. Think of it this way. No matter how small step you take in the x-direction, your y-increase will always be infinetely large, the line is vertical.

5. can you answer my last question exactly? is it always accepted that way with horizontal and vertical lines?

6. Originally Posted by furor celtica
can you answer my last question exactly? is it always accepted that way with horizontal and vertical lines?
Draw a graph. Draw the tangent at x = 0. Draw the normal at x = 0. The answer should be clear.