Position of a Point W.R.T Parabola

Q. The equation of a parabola is $y^2=4x$. Let P (1, 3) and Q (1, 1) are two points in the xy plane. Then,

1. P and Q are exterior points
2. P is an interior point while Q is an exterior point
3. P and Q are interior points
4. P is an exterior point while Q is an interior point

Q.

Which of the following can be the parametric equation of $x^2=4ay$

1. (at², 2at)

2. (2at, at²)

3. (-2at, at²)

4. (at², -2at)

Q.

The range of $\lambda$ if the point $(\lambda ,\lambda +1)$ lies inside the parabola $y^2=14x$

1. $(\frac{12-\sqrt{140}}{2},\frac{12+\sqrt{140}}{2})$

2. $(\frac{14-\sqrt{190}}{2},\frac{14+\sqrt{190}}{2})$

3. $(6,8)$

4. $(\frac{12-\sqrt{140}}{2},\frac{14+\sqrt{190}}{2})$

Q. $\mathrm{The}\mathrm{value}\mathrm{of}a\mathrm{for}\mathrm{which}\mathrm{the}\mathrm{point}(a,2a)\mathrm{lies}\mathrm{in}\mathrm{the}\mathrm{interior}\mathrm{region}\mathrm{of}\mathrm{the}\mathrm{parabola}{y}^2=16x\mathrm{is}$
.

1. $0<a<4$
2. $0<a<8$
3. $-4<a<0$
4. $-8<a<0$

Q. The point (-1, 7) does not lie inside the parabola $y^2$ = 12x.

1. False
2. True

Q. The point $(-2m,m+1)$ is an interior point of the smaller region bounded by the circle $x^2+y^2=4$ and the parabola $y^2=4x$. Then $m$ belongs to the intyerval

1. $-5-2\sqrt{6}<m<1$
2. $0<m<4$
3. $-1<m<\frac{3}{5}$
4. $-1<m<-5+2\sqrt{6}$

Q. Let the curve $C$ be the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $A$ and $B$ are the points of intersection of $C$ with the line $y=–5$, then the distance between $A$ and $B$ is

Q. Set of values of $a$ for which point $P(2,4)$ lies inside the parabola $y^2=4ax$ is

1. $a\in (-\infty ,-2)$
2. $a\in (-2,\infty )$
3. $a\in (2,\infty )$
4. $a\in (-\infty ,2)$

Q. Consider the parabola, $(y+3{)}^2=2(x-5)$, then the correct option(s) among the following is/are

1. point $(5,-3)$ lies on the parabola
2. point $(2,3)$ lies inside the parabola
3. point $(0,4)$ lies outside the parabola
4. point $(8,-2)$ lies inside the parabola

Q. If point $(k,k+2)$ lies inside the region bounded by parabolas $x^2=4(y+2)$ and $x^2=-(y-4)$ in first quadrant, then $k$ lies in the interval

1. $(0,2+2\sqrt{5})$
2. $(-2,0)$
3. $(0,1)$
4. $(2-2\sqrt{5},2+2\sqrt{5})$