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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 
?
?- a)10
- b)12
- c)14
- d)16
Correct answer is option 'A'. Can you explain this answer?
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In the xy-plane, the parabola with equation y = (x − 11)2 inters...
Choice A is correct. Substituting 25 for y in the equation y = (x − 11)2 gives 25 = (x − 11)2.
It follows that x − 11 = 5 or x − 11 = −5, so the x-coordinates of the two points of intersection are x = 16 and x = 6, respectively.
Since both points of intersection have a y-coordinate of 25, it follows that the two points are (16, 25) and (6, 25).
Since these points lie on the horizontal line y = 25, the distance between these points is the positive difference of the x-coordinates: 16 − 6 = 10.
Choices B, C, and D are incorrect and may be the result of an error in solving the quadratic equation that results when substituting 25 for y in the given quadratic equation.
It follows that x − 11 = 5 or x − 11 = −5, so the x-coordinates of the two points of intersection are x = 16 and x = 6, respectively.
Since both points of intersection have a y-coordinate of 25, it follows that the two points are (16, 25) and (6, 25).
Since these points lie on the horizontal line y = 25, the distance between these points is the positive difference of the x-coordinates: 16 − 6 = 10.
Choices B, C, and D are incorrect and may be the result of an error in solving the quadratic equation that results when substituting 25 for y in the given quadratic equation.
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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 ?a)10b)12c)14d)16Correct answer is option 'A'. Can you explain this answer?
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