Question

In the xy, y-plane, the parabola with equation y = ( x− 11)^2y=(x−11) 2 y, equals, (, x, −, 11, ), squaredintersects the line with equation y = 25y=25y, equals, 25 at two points, AAA and BBB. What is the length of \overline{AB} AB start overline, A, B, end overline?

Answer 1

Answer:

10 units

Step-by-step explanation:

Allow me to revise your question for a better understanding.

"In the xy-plane, the parabola with equation y = (x − 11) ² intersects the line with equation y = 25 at two points, A and B. What is the length of AB"  

Here is my answer

Because the  parabola intersects the line with equation y = 25  Substituting y = 25 in the equation of the parabola y = (x - 11)², we get

25 = (x - 11)²

<=>x - 11 = ± 5  

<=> $\left \{ {{x=6} \atop {x=16}} \right.$

Thus A(16, 25) and B(6, 25) are the points of intersection of the given parabola and the given line.

So the length of AB = √[(16 - 6)² + (25 - 25)²]

= √100 = 10 units

Answer 2

Answer:

10 units

Step-by-step explanation:

Allow me to revise your question for a better understanding.

"In the xy-plane, the parabola with equation y = (x − 11) ² intersects the line with equation y = 25 at two points, A and B. What is the length of AB"  

Here is my answer

Because the  parabola intersects the line with equation y = 25  Substituting y = 25 in the equation of the parabola y = (x - 11)², we get

25 = (x - 11)²

<=>x - 11 = ± 5  

<=>

Thus A(16, 25) and B(6, 25) are the points of intersection of the given parabola and the given line.

So the length of AB = √[(16 - 6)² + (25 - 25)²]

= √100 = 10 units