If the normal at any point to the curve `x^((2)/(3))+y^((2)/(3))=a^((2)/(3))` makes an angle `phi` with the x-axis, then prove that the equation of the normal is `ycosphi-xsinphi=acos2phi`.

If the normal at any point to the curve x^(2//3)+y^(2//3)=a^(2//3) makes an angle phi with the x-axis then prove that the equation of the normal is y cos phi- x sin phi = a cos 2phi .

If the normal to the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) at any point makes an angle phi with posititive direction of the x-axix, prove that, the equastion of the normal is y cos phi- x sin phi= a cos 2 phi

Find the equation of the tangent to the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) at the point (alpha,beta)

The normal at the point (1,1) on the curve 2y + x^(2) = 3 is

Prove theat the tangent drawn at any point to the curve f(x)=x^(5)+3x^(3)+4x+8 would make an acute angle with the x-axis.

The normal to the curve, x^(2)+2xy-3y^(2)=0 at (1, 1)-

Find the equations of the tangent and normal to the curve x^(2/3)+y^((2)/(3))=2 at (1,1).

A normal to the parabola y^(2)=5x makes an angle 45^(@) with the x-axis. Find the equation of the normal and the cooridnates of its foot.

Find the equation of the normal at the points on the curve y=(x)/(1-x^(2)) , where the tangent makes an angle 45^(@) with the axis of x.

find equation of normal at point (am^2, am^3) to the curve ay^2=x^3