Any equation have form like [tex]y^{2}=4ax[/tex], is known as equation of parabola.
Option A is correct.
Given curve is, [tex]y=x^{2}[/tex]
Now, check which of the given points does not lie on the given curve.
A. [tex](\frac{3}{2},\frac{9}{2} )[/tex] substitute in given curve.
[tex](\frac{9}{2} )=(\frac{3}{2} )^{2}[/tex] ⇒ [tex]\frac{9}{2}=\frac{9}{4}[/tex] , this is invalid .
Thus, point A is does not lie on the given curve.
B. (-1,1) substitute in equation of curve
[tex]1=(-1)^{2}[/tex]⇒ [tex]1=1[/tex] , this is valid
Thus, point B lies on given curve.
C. (4, 16) substitute in equation of curve.
[tex]16=16[/tex], this is valid
Thus, point C is lies on given curve.
D. [tex](\frac{1}{2},\frac{1}{4} )[/tex] substitute in equation of curve.
[tex]\frac{1}{4}=(\frac{1}{2} )^{2}[/tex] ⇒ [tex]\frac{1}{4} =\frac{1}{4}[/tex] , this is valid.
Thus, point D lies on given curve.
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