Find the lengths of the (i) tangent, (ii) normal, (iii) sub-tangent and (iv) sub-normal at any point P(a,b) on the parabola `y^2=2px (p>0`

The lengths of the sub-tangent , ordinate and the sub-normal are in

If L_(T), L_(N), L_(ST) and L_(SN) denote the lengths of tangent, normal, sub-langent and sub-normal respectively, ofa curve y =f(x) at a point P (2009, 2010) on it, then

If the length of the sub tangent is 9 and the length of the sub normal is 4 at (x, y) on y=f(x) then |y|=

Statement 1: The line ax+by+c=0 is a normal to the parabola y^(2)=4ax. Then the equation of the tangent at the foot of this normal is y=((b)/(a))x+((a^(2))/(b)). Statement 2: The equation of normal at any point P(at^(2),2at) to the parabola y^(2)= 4ax is y=-tx+2at+at^(3)

Find the equations of the tangent and normal to the given curve at the given points. (iv) y = x^(2) at (0,0).

Find the equations of the tangent and normal to the parabola y^(2)=4ax at the point (at^(2), 2at) .

Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) meet the x-axis at T and N respectively. If the lengths of sub-tangent and sub-normal at this point are equal, then the area of DeltaPTN is given by

Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) meet the x-axis at T and N respectively. If the lengths of sub-tangent and sub-normal at this point are equal, then the area of DeltaPTN is given by

At any point on the curve y=f(x) ,the sub-tangent, the ordinate of the point and the sub-normal are in