It is known that the parabola y = x ^ 2 + 2x + B intersects the X axis at two points a and B, and makes a circle with ab as the diameter (1) Find the value range of real number B (2) The equation of making circle with ab as diameter (3) If the vertex of C1 is inside the circle C2, find the value range of real number B I saw the process on the Internet, but I still don't understand it 1. Given that the parabola intersects with the X axis, then y = 0 is obtained by 0, then x ^ 2 + 2x + B = 0, because there are two points at the intersection, so there are two roots. According to the discriminant B ^ 2-4ac > 0, i.e. 2 ^ 2-4 * 1 * b > 0, we can get the root number 4-4b of B, i.e. y = 1-2 + b > 2 root number 1-b. after finding out the range of B, we can get the root number 4-4b of B, i.e. y = 1-2 + b > 2, and

It is known that the parabola y = x ^ 2 + 2x + B intersects the X axis at two points a and B, and makes a circle with ab as the diameter (1) Find the value range of real number B (2) The equation of making circle with ab as diameter (3) If the vertex of C1 is inside the circle C2, find the value range of real number B I saw the process on the Internet, but I still don't understand it 1. Given that the parabola intersects with the X axis, then y = 0 is obtained by 0, then x ^ 2 + 2x + B = 0, because there are two points at the intersection, so there are two roots. According to the discriminant B ^ 2-4ac > 0, i.e. 2 ^ 2-4 * 1 * b > 0, we can get the root number 4-4b of B, i.e. y = 1-2 + b > 2 root number 1-b. after finding out the range of B, we can get the root number 4-4b of B, i.e. y = 1-2 + b > 2, and

The symmetry axis of parabola is - B / 2A = - 2 / 2 = - 1, that is, the center of the circle is (- 1,0). According to the root formula, we get x = - 1 ± √ (1-B) and the radius is √ (1-B), that is, the equation of the circle is (x 1) &# 178; = 1-b
The third question is substituting x = - 1 into the parabola to get y = B-1. The vertex of the parabola is in the circle, so Lyl

Given that the line L: 2x-y-1 = 0 and parabola C: y2 = 6x intersect at two points a and B, the equation of circle with diameter AB is solved
Please help me,

First, solve the equations 2x-y-1 = 0 and Y ^ 2 = 6x by solving two intersection points. The coordinates of two points are: [(5 + √ 21) / 4, (3 + √ 21) / 2] and [(5 - √ 21) / 4, (3 - √ 21) / 2]. The center of the circle is the midpoint of AB, the coordinates are (5 / 4,3 / 2) the diameter of the circle is ab, the length = (3 √ 14) / 2, the radius = (3 √ 14) / 4, and the equation of the circle is (X-5 / 4) ^ 2 + (Y-3 /

Taking the right vertex of hyperbolic 16 parts x square - 9 parts y square = 1 as the vertex and the left focus as the focus, the parabolic equation is

According to the meaning of the title, taking (- 5,0) as the focus and (4,0) as the vertex, we can know that | P | = 18, its opening is to the left of the Y axis, and we can know that its basic function is y ^ 2 = - 2px, that is, y ^ 2 = - 36x, at this time, the vertex is (0,0), so we can get the equation y ^ 2 = - 36 (x-4) by moving four units to the right,

It is known that the axis symmetry of the parabola y = ax & # 178; + BX + C (a ≠ 0) is x = 1, and one of the equations ax & # 178; + BX + C = O is x = 3,
(1) Find another root of the equation AX & # 178; + BX + C = 0; (2) if the intersection of the parabola and the y-axis is (0,3), find the maximum value of the function

(1) Axis of symmetry x = - B / 2A = 1
So the two are symmetric with respect to x = 1
(x2+3)/2=1
x2=-1
The other one is - 1
(2)c=3
b=-2a
The maximum value is a + B + C = - A + 3
Y = a (x + 1) (x-3) through (0,3)
a(0+1)(0-3)=3
a=-1
Substitute:
The maximum value is - A + 3 = 1 + 3 = 4