The slope at any point of a curve $y=f\left( x \right)$ is given by $\dfrac { dy }{ dx } =3{ x }^{ 2 }$ and it passes through $\left( -1,1 \right)$. The equation of the curve is

$f(x)=\sin x$ একটি ত্রিকোণমিতিক ফাংশন এবং $M=x-2$ একটি বীজগাণিতিক রাশি।

If the tangent at any point ;$P(4m^{2}, 8m^{3})$ of $x^{3}-y^{3}=0$ is also a normal to the curve & ; $x^{3}-y^{3}=0$ , then value of m is-

The angle at which the curve $y={ x }^{ 2 }$ and the curve $x=\cfrac { 5 }{ 3 } \cos { t } ,y=\cfrac { 5 }{ 4 } \sin { t }$ intersect is

The curve for which the ratio of the length of the segment by any tangent on the $Y-$axis to the length of the radius vector is constant $(K)$, is