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The eccentricity of ellipse e: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is e, P is the point on e, from P to the circle x ^ 2 + y ^ 2 = B ^ 2, make tangent PA and Pb, a and B are tangent points, Ask if there is a point P, so that PA ⊥ Pb? If there is, calculate the point P coordinate; if not, explain the reason
Let P point coordinate (x1, Y1), the slope of PA and Pb be K and - 1 / K, the linear equations are y = KX + y1-kx1, y = - X / K + Y1 + X1 / K, and x ^ 2 + y ^ 2 = B ^ 2 to form the equations, tangent Δ = 0, the solutions are: B & # 178; + B & # 178; K & # 178; - (Y1) &# 178; + 2kx1y1-k & # 178; (x1) &# 178; = 0, B & # 178; + B & # 178; K & # 178
RELATED INFORMATIONS
- 1. It is known that there are two points a (1,3), B (3,0) in the ellipse X225 + y216 = 1, and P is a point on the ellipse, then the maximum value of | PA | + | Pb | is______ ．
- 2. It is proved that the line connecting the two tangent points must pass through a certain point Such as the title
- 3. Given the point Q (2,0) and the circle O: X & # 178; + Y & # 178; = 1, the ratio of the tangent length from the moving point m to the circle to | MQ | is root 2, the trajectory equation of the moving point m is obtained For detailed explanation, please refer to the attached figure,
- 4. Given the point Q (2,0) and the circle C: x2 + y2 = 1 on the rectangular coordinate plane, when the ratio of the tangent length from the moving point m to the circle and MQ is 1 or 2 respectively, the trajectory equation of the point m is obtained
- 5. If the distance between point m and point F (4,0) is less than 1, then the trajectory equation of point m is______ ．
- 6. The distance between two fixed points is 6, and the sum of the squares of the distances from point m to these two fixed points is 26. Find the trajectory equation of point M
- 7. Teacher worldbl: the distance from the moving point m (x, y) to the y-axis is less than the distance from it to the fixed point (2,0). Find the trajectory equation of the moving point m (x, y)
- 8. If the distance from the moving point P to the x-axis is 2 less than the distance to the fixed point F (0,2), then the trajectory equation of the moving point is obtained
- 9. The trajectory equation of a point whose distance from the X axis is equal to 2 is
- 10. Find the trajectory equation of the point whose distance from the Y axis is equal to 4
- 11. The projection of a point on the coordinate axis of the space coordinate system How to find. Can give an example to illustrate, as long as I can understand. Success can be + points How to find it when drawing
- 12. In Cartesian coordinates, the distance from the point P (- 1, (√ 3) / 2) to the origin o is
- 13. In Cartesian coordinates, the distance OP from point P (- 2,3) to the origin=______ ．
- 14. In the space rectangular coordinate system, the point a (1,0,2) B (1, - 3, - 1) m is on the Y axis, and the distance to a and B is equal In the space rectangular coordinate system, if the point a (1,0,2) B (1, - 3, - 1) m is on the Y axis and the distances to a and B are equal, then the coordinate of M is?
- 15. Given that the distance from the moving point P to the fixed point F (3,0) and to the fixed value line x = 5 / 2 is constant 2 √ 3 / 3, the trajectory equation of point P is obtained Urgent``
- 16. Two fixed points a (- C, 0), B (C, 0). The sum of the distances from the moving point P to the two fixed points is a constant 2A. Find the trajectory equation of point P
- 17. There are two fixed points a and B in the plane, and | ab | = 2. The ratio of the distance between a moving point m and two points a and B in the plane is 2:1
- 18. The trajectory of a point whose distance from the plane to the fixed point O is equal to 2cm is ()
- 19. Nowadays, there are many devices using batteries as power supply, and the amount of batteries used is very large. Some of them are rechargeable batteries, such as battery car batteries and automobile batteries. These rechargeable batteries all have one feature: the newly purchased batteries can be used for a long time after charging. After long-term use, they will be fully charged, and the power will soon run out. Please use Ohm's law of the whole circuit for analysis! Thank you for your explanation!
- 20. Calculation of maximum power of sliding rheostat by Ohm's law of closed loop If the sliding rheostat is connected in parallel with a resistor, how can the resistor be equivalent to the internal resistance