Graph (x-2)/5+((y-5)^2)/5=1

x-25+(y-5)25=1
Combine the numerators over the common denominator.
x-2+(y-5)25=1
Multiply both sides of the equation by 5.
5⋅x-2+(y-5)25=5⋅1
Simplify both sides of the equation.
Cancel the common factor of 5.
Cancel the common factor.
5⋅x-2+(y-5)25=5⋅1
Rewrite the expression.
x-2+(y-5)2=5⋅1
x-2+(y-5)2=5⋅1
Multiply 5 by 1.
x-2+(y-5)2=5
x-2+(y-5)2=5
Move all terms not containing x to the right side of the equation.
Add 2 to both sides of the equation.
x+(y-5)2=5+2
Subtract (y-5)2 from both sides of the equation.
x=5+2-(y-5)2
Add 5 and 2.
x=7-(y-5)2
x=7-(y-5)2
Find the properties of the given parabola.
Reorder 7 and -(y-5)2.
x=-(y-5)2+7
Use the vertex form, x=a(y-k)2+h, to determine the values of a, h, and k.
a=-1
h=7
k=5
Since the value of a is negative, the parabola opens left.
Opens Left
Find the vertex (h,k).
(7,5)
Find p, the distance from the vertex to the focus.
Find the distance from the vertex to a focus of the parabola by using the following formula.
14a
Substitute the value of a into the formula.
14⋅-1
Cancel the common factor of 1 and -1.
Rewrite 1 as -1(-1).
-1(-1)4⋅-1
Move the negative in front of the fraction.
-14
-14
-14
Find the focus.
The focus of a parabola can be found by adding p to the x-coordinate h if the parabola opens left or right.
(h+p,k)
Substitute the known values of h, p, and k into the formula and simplify.
(274,5)
(274,5)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
y=5
Find the directrix.
The directrix of a parabola is the vertical line found by subtracting p from the x-coordinate h of the vertex if the parabola opens left or right.
x=h-p
Substitute the known values of p and h into the formula and simplify.
x=294
x=294
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Left
Vertex: (7,5)
Focus: (274,5)
Axis of Symmetry: y=5
Directrix: x=294
Direction: Opens Left
Vertex: (7,5)
Focus: (274,5)
Axis of Symmetry: y=5
Directrix: x=294
Select a few x values, and plug them into the equation to find the corresponding y values. The x values should be selected around the vertex.
Substitute the x value 5 into f(x)=-(x-7)+5. In this case, the point is (5,6.41421356).
Replace the variable x with 5 in the expression.
f(5)=-((5)-7)+5
Simplify the result.
Simplify each term.
Subtract 7 from 5.
f(5)=2+5
Multiply -1 by -2.
f(5)=2+5
f(5)=2+5
The final answer is 2+5.
y=2+5
y=2+5
Convert 2+5 to decimal.
=6.41421356
=6.41421356
Substitute the x value 5 into f(x)=–(x-7)+5. In this case, the point is (5,3.58578643).
Replace the variable x with 5 in the expression.
f(5)=–((5)-7)+5
Simplify the result.
Simplify each term.
Subtract 7 from 5.
f(5)=-2+5
Multiply -1 by -2.
f(5)=-2+5
f(5)=-2+5
The final answer is -2+5.
y=-2+5
y=-2+5
Convert -2+5 to decimal.
=3.58578643
=3.58578643
Substitute the x value 6 into f(x)=-(x-7)+5. In this case, the point is (6,6).
Replace the variable x with 6 in the expression.
f(6)=-((6)-7)+5
Simplify the result.
Simplify each term.
Subtract 7 from 6.
f(6)=1+5
Multiply -1 by -1.
f(6)=1+5
Any root of 1 is 1.
f(6)=1+5
f(6)=1+5
Add 1 and 5.
f(6)=6
The final answer is 6.
y=6
y=6
Convert 6 to decimal.
=6
=6
Substitute the x value 6 into f(x)=–(x-7)+5. In this case, the point is (6,4).
Replace the variable x with 6 in the expression.
f(6)=–((6)-7)+5
Simplify the result.
Simplify each term.
Subtract 7 from 6.
f(6)=-1+5
Multiply -1 by -1.
f(6)=-1+5
Any root of 1 is 1.
f(6)=-1⋅1+5
Multiply -1 by 1.
f(6)=-1+5
f(6)=-1+5
Add -1 and 5.
f(6)=4
The final answer is 4.
y=4
y=4
Convert 4 to decimal.
=4
=4
Graph the parabola using its properties and the selected points.
xy56.4153.59666475
xy56.4153.59666475
Graph the parabola using its properties and the selected points.
Direction: Opens Left
Vertex: (7,5)
Focus: (274,5)
Axis of Symmetry: y=5
Directrix: x=294
xy56.4153.59666475
Graph (x-2)/5+((y-5)^2)/5=1