Slope Point Form of a Line

Q. The area bounded by the parabola $y=4-x^2$ and $X$-axis in sq units is:

1. $\frac{32}{3}$
2. $\frac{8}{3}$
3. $\frac{1}{3}$
4. $\frac{16}{3}$

Q. If the line $y=mx+a$ meets the parabola $y^2=4ax$ at two points whose abscissa are $x_1$ and $x_2,$ then the value of $m$ for which $x_1+x_2=0$ is

Q. Let $y=f\left(x\right)$ is a parabola of the form $y=x^2+ax+1$ and tangent to the parabola at the point of intersection with $y-$axis also touches the circle $x^2+y^2=r^2$.If it is known that no point of the parabola is below $x-$axis then the radius of circle when $a$ attains its maximum value in units is

1. $\frac{1}{\sqrt{10}}$
2. $\frac{1}{\sqrt{5}}$
3. $1$
4. $\sqrt{5}$

Q. The number of distinct normals that can be drawn from $(-2,1)$ to the parabola $y^2-4x-2y-3=0$, is

1. $1$
2. $2$
3. $3$
4. $0$