As shown in the figure, the coordinates of a and B are a (2,1) and B (5,0) respectively. Find the area of △ OAB

As shown in the figure, the coordinates of a and B are a (2,1) and B (5,0) respectively. Find the area of △ OAB

According to the meaning of the title, the area of triangle OAB = 12 × 1 × 5 = 125

It is known that the chord length ab of a straight line y = 2x + K cut by a parabola x2 = 4Y is 20, and O is the coordinate origin
1. By substituting y = 2x + K into x ^ 2 = 4Y, x ^ 2-8x-4k = 0, ⊿ 0, k > - 4 is obtained,
|Ab | = 4 √ 5 √ (K + 4) = 20, k = 1
What's the original formula of chord length? I can calculate x1x2 = - 4, X1 + x2 = 8, but not k = 1~~

Chord length formula AB = root sign (1 + K ^ 2) times root sign [(x1 + x2) ^ 2-4x1x2)]

We know that the line L: y = x + A is tangent to the parabola C: x ^ 2 = 4Y at point A. 1: find the value of the real number A. 2: find the point a as the center of the circle and the parabola C
It is known that the line L: y = x + A and the parabola C: x ^ 2 = 4Y are tangent to point a
1: Find the value of the real number a
2: Find the equation of the circle with point a as the center and tangent to the Quasilinear of parabola C

x^2＝4(x＋a),x^2-4x-4a=0
4 ^ 2 + 16A = 0, a = - 1, y = X-1. X ^ 2 = 4Y
x=2,y=1,A(2,1)
X ^ 2 = 4Y, the Quasilinear equation is y = - 1
So the radius of the circle is two
The equation of circle is: (X-2) ^ 2 + (Y-1) ^ 2 = 4
x^2+y^2-4x-2y+1=0