Given Q (0,4), P is the minimum absolute value of PQ at any point on y = x ^ 2 + 1

Because P is a point on y = x ^ 2 + 1, let P (x, x ^ 2 + 1)
So PQ ^ 2 = x ^ 4-5x ^ 2 + 9 = (x ^ 2-2.5) ^ 2 + 11 / 4
So the minimum value of PQ ^ 2 is 11 / 4, so the minimum value of PQ is 11 / 4 under the root

RELATED INFORMATIONS

1. Given the real number x, y satisfies the relation: x2 + y2-2x + 4y-20 = 0, then the minimum value of x2 + Y2 is 30-10530-105
2. The maximum value of real numbers x, y satisfying X & sup2; + Y & sup2; - 2x-4y-20 = 0, X & sup2; + Y & sup2; is
3. P is a point in the rectangle ABCD (as shown in the figure). The area of the triangle PAB is equal to 5, and the area of the triangle PBC is equal to 13. Q: what is the area of the triangle PBD?
4. The formula of common practical problems in junior middle school For example: itinerary problems, encounter problems, it is best to have examples and detailed analysis!
5. (1) 4,16,36,64, (), 144196... () (100th number); (2) 2,5,10,17,26..., () (50th number)
6. I borrowed a book from the library
7. Find the function f (x) = (1 + 1 / x) ^ x, when x = ± 10, x = ± 100, x = ± 1000, x = ± 10000, what is f (x) = number?
8. My mother said to me, "I'm going to work overtime tonight. You can cook your own dinner."
9. (answer as many questions as you can) 1. Mr. Wang took the train from Beijing station to Guangzhou. Ten hours later, the train traveled five fifths of the whole journey. How long does it take from Beijing to Guangzhou? 2. Li Di can input 30 Chinese characters in two-thirds of a minute. According to this calculation, how many Chinese characters can he input in half an hour? 3. Congcong walked 60 meters in five sixths of a minute. At this speed, how many meters can he walk in three fourths of an hour? 4. A piece of land has 10 hectares, which can be cultivated in 0.75 hours with two tractors. How many hectares can each tractor cultivate per hour?
10. Xinhua Bookstore imported 2800 literature and art books, 175 less than 7 / 8 of the science and technology books. How many science and technology books did the bookstore import? Use the equation to solve the problem
11. Let P (x, y) be a point on the ellipse x ^ 2 + 4Y ^ 2 = 16, then the maximum value of X + y is equal to
12. Let P (x, y) be a moving point on the ellipse x216 + Y29 = 1, then the maximum value of X + y is______ ．
13. Given that point a (0,1) is a point on the ellipse x2 + 4y2 = 4 and point P is a moving point on the ellipse, the maximum length of chord AP is () A. 233B. 2C. 433D. 4
14. Let p be a point on the ellipse x ^ / 25 + y ^ / 9 = 1 and Q R be a point on the circle (x + 4) ^ + y ^ = 1 / 4 and (x-4) ^ + y ^ = 1 / 4 respectively, then what is the minimum value of PQ + PR,
15. Given that P is the point on the ellipse X225 + Y29 = 1, Q and R are the points on the circle (x + 4) 2 + y2 = 14 and (x − 4) 2 + y2 = 14 respectively, then the minimum value of | PQ | + | PR | is () A. 89B. 85C. 10D. 9
16. It is known that there is a point (4, - 1) in the ellipse x ^ 2 / 25 + y ^ 2 / 9 = 1, f is the right focus, M is the moving point on the ellipse, and the minimum value of Ma + MF (detailed explanation)
17. Given the nonnegative integers x, y, Z, satisfying (x-1) / 2 = (6-y) / 3 = (Z-3) / 4, let w = 3x + 4Y + 5Z, find the maximum and minimum of W?
18. Given that non negative integers x, y, Z satisfy X-1 / 2 = 6-y / 3 = Z-3 / 4, let w = 3x + 4Y + 5Z, find the maximum and minimum of W
19. There are two different intersection points between the straight line y = x + m and the ellipse 2x square + y square = 1. Find the value range of the real number M
20. It is known that there are two intersections between the straight line y = 2x + m and the ellipse x ^ 2 / 9 + y ^ 2 / 4 = 1, so the value range of the real number m can be obtained