Question

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

• A. point $(5,-3)$ lies on the parabola
• B. point $(2,3)$ lies inside the parabola
• C. point $(0,4)$ lies outside the parabola
• D. point $(8,-2)$ lies inside the parabola

Answer 1

Answer: (A), (C), (D)

point $(8,-2)$ lies inside the parabola

If the point $(x_1,y_1)$ lies inside the parabola, then $(y_1+3{)}^2-2(x_1-5)<0$
If the point $(x_1,y_1)$ lies on the parabola, then $(y_1+3{)}^2-2(x_1-5)=0$
If the point $(x_1,y_1)$ lies outside the parabola, then $(y_1+3{)}^2-2(x_1-5)>0$

For point $(5,-3)$
$(-3+3{)}^2-2(5-5)=0$
It lies on the parabola.

For point $(2,3)$
$(3+3{)}^2-2(2-5)>0$
It lies outside the parabola.

For point $(0,4)$
$(4+3{)}^2-2(0-5)>0$
It lies outside the parabola.

For point $(8,-2)$
$(-2+3{)}^2-2(8-5)<0$
​​​​​​​It lies inside the parabola.