If the point (m, n) is on ax + by + 2C = 0, find the minimum value of m ^ 2 + n ^ 2

If the point (m, n) is on ax + by + 2C = 0, find the minimum value of m ^ 2 + n ^ 2

M ^ 2 + n ^ 2 is the square of the distance from the origin to the point (m, n)
Let the distance between the origin and the line be d
Since m is on a definite line, m ^ 2 + n ^ 2 > = D ^ 2
The linear equation is ax + by + 2C = 0
From the formula of distance from point to line, we can get
D = | 0 + 0 + 2C | / radical (a ^ 2 + B ^ 2) = 2C / C = 2
So the minimum value of m ^ 2 + n ^ 2 is 4

A, B, C are the sides of right triangle, C is the hypotenuse, and (m, n) find the minimum value of M2 + N2 on ax + by + 2C = 0

M2 + N2 is the square of the distance from (m, n) to the origin

It is known that the three sides of a triangle are N2 + 1, n2-1 and 2n respectively. Is the triangle a right triangle? If it is a right triangle, please indicate which side is opposite to the angle
The angle is a right angle

(n^2-1)^2+(2n)^2
=n^4-2n^2+1+4n^2
=n^4+2n^2+1
=(n^2+1)^2
A triangle is a right triangle
The angle that N2 + 1 faces is a right angle