Given that the line y = MX + 1 and the curve y = x ^ 2-m intersect at two different points a and B, then the trajectory equation of point m in line AB is obtained

Given that the line y = MX + 1 and the curve y = x ^ 2-m intersect at two different points a and B, then the trajectory equation of point m in line AB is obtained

If y = MX + 1y = x ^ 2-m is (x + 1) (x-m-1) = 0, then X1 = - 1, X2 = m + 1 (M is not - 2) corresponds to Y1 = - M + 1, y2 = m ^ 2 + m + 1, then the coordinate of M is XM = (x1 + x2) / 2 = m / 2ym = (Y1 + Y2) / 2 = (m ^ 2) / 2 + 1 (M is not - 2, that is, X is not - 1). Finally, replace m with X to get y = 2 * (x ^ 2) + 1 (x is not - 1)

Write out all positive integer solutions of the equation 4x + y = 20
Note that it's a positive integer!

Direct generation
Y = 20, x = 0 (not true)
x=1,y=16
x=2,y=12
x=3,y=8
x=4,y=4
X = 5, y = 0 (not true)

Why is an ellipse defined mathematically as "the locus of a point in the plane whose sum of distances from two fixed points F1 and F2 is equal to a constant (greater than | F1F2 |)
Ellipse is a figure extracted from life. Why do mathematicians define ellipse in this way?
How to prove that all "ellipses" can find two fixed points, so that the sum of distances between all points on the ellipse and two fixed points F1 and F2 is equal to a constant?

I'm a junior in high school Love mathematics, you have the level of this problem, you can check the "ellipse definition" on Baidu, but can not solve your problem I think there is a rule in mathematics, that is, there is no reason for the basic definition, such as why one plus one is two, why the sum of the internal angles of a triangle is 180 degrees I don't think this

The application of factorization formula
1,4(a+b)²-25(a-b)²
2,(a+b)²-4a²
3,x³-16x
4, the fourth power of - x + 16
5,2ab³-2ab

Today is May 5, 2012. How many days are there before October 18, 2012?

There are 167 days from 0:00 on May 5, 2012 to 24:00 on October 18, 2012
There are 153 days from 0:00 on May 19, 2012 to 24:00 on October 18, 2012

A story about interesting mathematics. Seventy words

One day, Thales saw that people were reading the notice. He also went up to read it. The notice said that the Pharaon wanted to find the smartest person in the world to measure the height of the pyramid. Thales went to the Pharaon. The Pharaon asked Thales what tools he used to measure the pyramid. Thales said that he only used a stick and a ruler. Everyone thought it was very strange

The greater the pollution index is, the better the air quality will be and the more harmful it will be to human health

The higher the pollution index, the worse the air quality and the more obvious the impact on human health

On April 7, 2009, the State Council announced the "recent key implementation plan of medical and health system reform". A municipal government decided to invest 60 million yuan in improving medical and health services in 2009, an increase of 12.5 million yuan compared with 2008. The service objects of the investment include "demander" (patients, etc.) and "supplier" (medical and health institutions, etc.), and it is expected that the investment of "demander" will increase in 2009 (1) how many million yuan did the municipal government invest in improving medical and health services in 2008? (2) How many million yuan did the municipal government invest in "demander" and "supplier" in 2009? (3) The municipal government estimates that 72.6 million yuan will be invested in improving medical and health services in 2011. If the annual capital investment from 2009 to 2011 increases at the same growth rate, the annual growth rate from 2009 to 2011 can be calculated

What's the product of 52 times 52 out of 53?

52 out of 53 square

Under what circumstances is work efficiency regarded as unit 1 (Mathematics)
Why is the unit 1 after the word "Zhan", "Shi" and "Bi"?

The quantity after the word "Zhan", "Shi" and "Bi" is unit 1