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Tangent and Normal

Application of derivatives of Class 12

Tangent and Normal

Let y = f(x) be the equation of a curve and let P(x0, y0) be a point on the curve. Let PT be the tangent, PN the normal and PM be perpendicular to the axis of x.

The slope of the tangent to the curve y = f(x) at P is given by Tangent and Normal

and therefore the equation to the tangent to the curve y = f(x) at (x0, y0) is

y −y0 = Tangent and Normal

and the equation to the normal will be

y −y0 + Tangent and Normal(x −xo) = 0

Length of the tangent is PT = y0 cosecθ

Tangent and Normal

= y0 Tangent and Normal = y0 Tangent and Normal

and length of the normal is

y0 secθ = y0Tangent and Normal = y0Tangent and Normal

Likewise lengths of the subtangent and subnormal can also be calculated.

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