The angle between the curves $y^2=4x+4$ and $y^2=36(9-x)$ is (in $^{\circ}$)

The angle between the tangents to the curve $y = x^2 - 5x + 6$ at the points $(2, 0)$ and $(3, 0)$ is:

If the normal to the curve $y=f(x)$ at $(1,2)$ makes an angle $\frac{3 \pi}{4}$ with the positive $X$-axis,then $f^{\prime}(1)=$

On the curve $y=x^3$,the point at which the tangent line is parallel to the chord joining the points $(-1, -1)$ and $(2, 8)$ is

If $\beta$ is an angle between the normals drawn to the curve $x^2+3y^2=9$ at the points $P(3 \cos \theta, \sqrt{3} \sin \theta)$ and $Q(-3 \sin \theta, \sqrt{3} \cos \theta)$,where $\theta \in (0, \frac{\pi}{2})$,then:

If the tangent to the curve $y=x+\sin y$ at a point $(a, b)$ is parallel to the line joining $\left(0, \frac{3}{2}\right)$ and $\left(\frac{1}{2}, 2\right),$ then