The curve $y=a x^3+b x^2+c x+5$ touches the $X$-axis at $P(-2,0)$. Then,$c=$

The tangent to the curve $y = x^2 - 5x + 5$ which is parallel to the line $2y = 4x + 1$ also passes through the point

If the tangent to the curve $2y^3 = x^3 + ax^2$ at the point $(a, a)$ cuts off intercepts $\alpha$ and $\beta$ on the coordinate axes such that $\alpha^2 + \beta^2 = 61$, then the value of $a$ is

If the slope of the tangent drawn at any point $(x, y)$ to the curve $y=f(x)$ is $3x^2-5$ and $f(1)=2$, then the tangent at $(1, 2)$ to the curve $y=f(x)$ intersects the curve at the point

If the slope of the line through $(0,0)$ which is tangent to the curve $y=x^2+x+16$ is $m$,then the value of $m-4$ is

The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0$ is