Tangents and Normals
The derivative of the curve y = f ( x ) is f ‗( x ) which represents the slope of tangent and equation of the tangent to the curve at P is
where ( x , y ) is an arbitrary point on the tangent .
The equation of normal at ( x , y ) to the curve is
1 . If then the equations of the tangent and normal at ( x , y ) are ( Y – y ) = 0 and ( X – x ) = 0 , respectively .
2 . If then the equation of the tangent and normal at ( x , y ) are ( X – x ) = 0 and ( Y – y ) = 0 , respectively .
Slope of Tangent ( i ) If the tangent at P is perpendicular to x-axis or parallel to y-axis ,
( ii ) If the tangent at P is perpendicular to y-axis or parallel to x-axis ,