Substitute the given points one by one into all of the equation options.
A
Practice makes perfect
If the graph of the equation contains a point, then the point substituted into the equation will hold true. Instead of substituting every point into every equation, let's start by substituting one point into each equation and seeing which hold true. For simplicity let's start with the point (-4,0), because of y=0.
Equation
Substitute (-4,0)
Simplify
Is valid?
x^2+4y^2=16
( -4)^2+4( 0)^2? =16
16=16
Yes
4x^2+16y^2=144
4( -4)^2+16( 0)^2? =144
64 ≠144
No
4x^2+25y^2=64
4( -4)^2+25( 0)^2? =64
64=64
Yes
9x^2+4y^2=81
9( -4)^2+4( 0)^2? =81
144 ≠81
No
The equations 4x^2+16y^2=144 and 9x^2+4y^2=81 do not contain the point (- 4,0), so we have narrowed down our options to two equations. Let's substitute the next point (-2, ± sqrt(3)). Because of the y^\bm{2} in all the equations, y=sqrt(3) and y=- sqrt(3) will lead to the same values.
Equation
Substitute (-2,± sqrt(3))
Simplify
Is valid?
x^2+4y^2=16
( -2)^2+4( ± sqrt(3))^2? =16
16=16
Yes
4x^2+25y^2=64
4( -2)^2+25( ± sqrt(3))^2? =64
91 ≠64
No
The equation x^2+4y^2=16 is the only equation that contains the points (-4,0) and (-2, ± sqrt(3)). Let's substitute the remaining points into this equation to ensure it contains all the points in the table.
Points
x^2+4y^2=16
Simplify
Is valid?
(0, ± 2)
( 0)^2+4( ± 2)^2? =16
16=16
Yes
(2, ± sqrt(3))
(2)^2+4(± sqrt(3))^2? =16
16=16
Yes
(4,0)
(4)^2+4( )^2? =16
16=16
Yes
The graph of the equation x^2+4y^2=16 contains all the points in the given table. The correct answer is option A.
