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The equation of a circle whose center is on the parabola y ^ 2 = 4x (Y > 0) and is tangent to the Quasilinear and x-axis of the parabola is
The directrix of the parabola y & #178; = 4x is x = - 1. If the circle is tangent to the parabola directrix, then the distance from the center of the circle to the directrix is equal to the radius of the circle, and the distance from the center of the circle to the directrix is equal to the distance from the center of the circle to the focus, then the circle passes through the focus F of the parabola
The equation of a circle whose center is on the parabola y2 = 2x (Y > 0) and tangent to the Quasilinear and x-axis of the parabola is ()
A. x2+y2−x−2y−14＝0B. x2+y2+x-2y+1=0C. x2+y2-x-2y+1=0D. x2+y2−x−2y+14＝0
Let the coordinates of the center of the circle be (B22, b), then B22 + 12 = B & nbsp; can be obtained from the tangent of the circle to the Quasilinear and x-axis of the parabola; so B = 1, so the center of the circle is (12, 1) radius r = 1, so the equation of the circle whose center is on the parabola y2 = 2x (Y > 0) and tangent to the Quasilinear and x-axis of the parabola is (x − 12) 2 + (Y − 1) 2 & nbsp; = 1, that is, X2 + Y2 − x − 2Y + 14 = 0, so D is selected
The equation of a circle whose center is on the parabola y2 = 2x and tangent to the Quasilinear and x-axis of the parabola is
Let the center of the circle be m (x, y), then
Y = √ 2x, i.e. m (x, √ 2x)
The circle m is tangent to the directrix and x-axis
The inverted x-axis of M is equal to the distance to the guide line
∴x＋1／2＝√2x
∴x＝1／2,y＝±1
The circular equation is (x-1 / 2) &# 178; + (Y ± 1) &# 178; = 2
The equation of a circle whose center is on the parabola y = 2x and tangent to the x-axis and the Quasilinear of the parabola is?
There are two sets of solutions to this problem. If this point satisfies the meaning of the problem, then there is √ 2x = x + - 1 / 2 ｜ 2x = x + X + 1 / 4, and the solution is x = 1 / 2, so y = √ (2 × 1 / 2) = 1, r = x + 1 / 2 = 1. The equation of the circle is (x-1 / 2) + (Y-1) = 1 (2) P (x, √ 2x) is the point of the parabola at the bottom of the x-axis, If this point satisfies the meaning of the problem, then the solution of ｜ - √ 2x = x + ｜ - 1 / 2 ｜ 2x = x + X + 1 / 4 is x = 1 / 2, so y = - √ (2 × 1 / 2) = - 1, r = ｜ - √ 2X = 1, and the equation of circle is (x-1 / 2) + (y + 1) = 1
RELATED INFORMATIONS
- 1. The trajectory equation of the focus of a parabola passing through a fixed point (1,2) and taking the y-axis as the guide line is RT, great Xia, do me a favor
- 2. 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
- 3. If the parabola y = ax & # 178; + K (a is not equal to 0) and y = - 2x & # 178; + 4 are symmetric about X axis, find the value of a, K
- 4. If the ordinate of the lowest point of the parabola y = MX square + 2mx + 2m-1 is zero, then M=
- 5. When y = - x ^ 2 - (M-3) x + m is known, the distance between the two intersections of the parabola and X axis is equal to 3
- 6. If the parabola y = 2x2 + 8x + m has only one common point with the X axis, then the value of M is______ ．
- 7. If the parabola y = ax ^ 2 + BX + C is symmetric about the Y axis, then B =? How to distinguish the symmetry axis of quadratic function from X axis or Y axis?
- 8. If the parabola y = 2 (x + 3) (x + m) intersects with the x-axis and two points a and B (a is on the left side of B) and OA: OB = 3:1, find the value of M
- 9. (14 points) it is known that the vertex of the parabola y = AX2 + BX + C is a (3, - 3), and an intersection point with the X axis is B (1,0). (1) find the analytical formula of the parabola. (2) (2) P is a moving point on the parabola. Find the coordinates of the point P 0 which minimizes the sum of the distances from P to a and B (3) Let the other intersection of the parabola and the x-axis be c. is there a point m on the parabola such that the area of △ MBC is equal to one third of the area of the quadrilateral with points a, P 0, B and C as vertices? If it exists, request the coordinates of all eligible points m; if not, explain the reason
- 10. Given that the parabola y = - x2 + 2 (k-1) x + K + 2 intersects with the X axis and two points AB, and point a is on the negative half axis of the X axis, B is on the positive half axis of the X axis, Bo = 5ao, find the parabola
- 11. The equation of a circle whose center is on the parabola x ^ 2 = 2Y and is tangent to the Quasilinear and Y-axis of the parabola
- 12. Solving the parabolic standard equation (1) the focus is f (- 7,0) (2) the collimator is y = 4 (3) the axis of symmetry is x, and the distance from the vertex to the focus is equal to 6
- 13. Point m is a moving point on parabola y2 = x, and point n is a point on the curve C of the circle C1: (x + 1) 2 + (y-4) 2 = 1 symmetric with respect to the straight line X-Y + 1 = 0, then the minimum value of | Mn | is () A. 112−1B. 102−1C. 2D. 3−1
- 14. Parabola y = - 2x ^ + 3x-5 about x-axis, y-axis, origin after the symmetrical movement of the functional equations are? Hope to explain the knowledge points, need specific steps
- 15. It is known that the parabola y = x & # 178; - 6x + 5 (1) is the analytic expression of the parabola with respect to the y-axis symmetric image (2) is the analytic expression of the parabola with respect to the x-axis symmetric image
- 16. It is known that the symmetry axis of parabola y = AX2 + BX + C = - 1, intersects with X axis at two points a and B, intersects with y axis at C, where a (- 3,0), C (0,2) (1) Finding the function relation of parabola (2) Finding the coordinates of point B (3) There is always a point P on the symmetry axis, so that the perimeter of the triangle PBC is minimum, and the coordinates of point P are requested en
- 17. Let a and B be two points on the parabola X & # 178; = 2PY. The line AB passes through the focus F. if the vector OA * the vector ob = - 6, solve the parabolic equation
- 18. Given that the line L: y = x + m and parabola y2 = 8x intersect at two points a and B, (1) if | ab | = 10, find the value of M; (2) if OA ⊥ ob, find the value of M
- 19. As shown in the figure: the parabola intersects the x-axis at two points a (- 1,0) and B (3,0), and intersects the y-axis at points c (0, - 3). Let the vertex of the parabola be d (1) find the analytical formula of the parabola and the coordinates of vertex D: (2) prove that the center of the circumscribed circle of △ BCD falls at the midpoint of the BD side: (3) if point P is a moving point on the coordinate axis, it can make the triangle with P, a, C as the vertex similar to △ BCD? If it exists, Please write the coordinates of point P: if not, please explain the reason
- 20. Given the angle AOB = 130 degrees, OE bisecting angle BOC, of bisecting angle AOC, calculate the degree of angle EOF