# Equation of Tangents and Normals

Let*P*(

*x*

_{1},

*y*

_{1}) be any point on the curve

*y*=

*f*(

*x*).

If tangent at

*P*makes angle*Î¸*with positive direction of the*x*-axis, then*dy*/*dx*= tan*Î¸*.**Equation of tangent**Equation of tangent at point

*P*(

*x*

_{1},

*y*

_{1}) is

*y*â€“

*y*

_{1}=

**Equation of normal**Equation of normal at point

*P*(

*x*,

*y*) is

*y*â€“

*y*

_{1}=

*Notes:*- The point
*P*(*x*_{1},*y*_{1}) will satisfy the equation of the curve and the equation of tangent and normal line. - If the tangent at any point
*P*on the curve is parallel to the axis of*x*then*dy*/*dx*= 0 at the point*P*. - If the tangent at any point on the curve is parallel to the axis of
*y*, then*dy*/*dx*= âˆž or*dx*/*dy*= 0. - If the tangent at any point on the curve is equally inclined to both the axes then
*dy*/*dx*= Â±1. - If the tangent at any point makes equal intercept on the coordinate axes then
*dy*/*dx*= â€“1. - Tangent to a curve at the point
*P*(*x*_{1},*y*_{1}) can be drawn even though*dy*/*dx*at*P*does not exist.*x*= 0 is a tangent to*y*=*x*^{2/3}at (0, 0).