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

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

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

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

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