Proof: the distance from a point on an equiaxed hyperbola to the center of the hyperbola is the equal proportion median of its distance from the focus
Let the hyperbola be x ~ 2 / a ~ 2-y ~ 2 / a ~ 2 = 1, and the square of the distance from any point (x0, Y0) to the center is equal to x0 ~ 2 + Y0 ~ 2, because x ~ 2-y ~ 2 = a ~ 2 and both sides add x ~ 2 + y ~ 2-A ~ 2, then the product of x0 ~ 2 + Y0 ~ 2 = 2x0 ~ 2-A ~ 2 to two focal points is equal to | (ex + a) (ex-a) | because e = root 2, so | (ex0 + a) (ex0 -
RELATED INFORMATIONS
- 1. Proof: the distance from any point on an equiaxed hyperbola to the center of symmetry is the equal proportion median of the distance from him to two focal points
- 2. Shouldn't the distance difference between any point on the hyperbola and two focal points be equal to the length of focal length Shouldn't the distance difference between any point on the hyperbola and two focal points be equal to the focal length? Why is it equal to 2A?
- 3. Find a point on the hyperbola x ^ 2 / 16-y ^ 2 / 9 = 1, so that the distance between the point and the left focus is equal to twice the distance between the point and the right focus
- 4. Who knows: what is the inflection point of the curve y = (1-x) ^ 3?
- 5. Find the inflection point of the curve y = (x-1) ^ (5 / 3)
- 6. Inflection point of function y = Xe ^ (- x ^ 2)
- 7. The inflection point of graph of function y = xe-x is______ .
- 8. It is proved that the inflection point of the curve y = xsinx must be on the curve y ^ 2 (4 + x ^ 2) = 4x ^ 2
- 9. It is proved that the curve y = (x-1) / (x ^ 2 + 1) has three inflection points, and the three inflection points lie on the same straight line,
- 10. It is proved that the curve y = (x + 1) / (x ^ 2 + 1) has three inflection points on the same line After getting the second derivative of the function, I don't know how to get all three points
- 11. The distance from a point P on the square of nine times x minus one sixteenth of y to its left quasilinear is 4.5, then the distance from point P to its right focus? I forgot about this kind of question, what is the standard line,
- 12. If the distance from a point P on hyperbola x2-y23 = 1 to the left focus is 4, then the distance from point P to the right collimator is () A. 1b. 2C. 3D. 1 or 3
- 13. The distance between a point P on hyperbola X & sup2 / 64-y & sup2 / 64 = 1 and its right focus is 8, then the distance between point P and its left quasilinear () A.10 B.32√7/7 C.12√2 D.32/5 From the known a & sup2; = B & sup2; = 64, we get e = √ 2, a & sup2 / / C = 4 √ 2. So the distance from point P to the right focus is 8 / E = 4 √ 2. And because a & sup2 / / C = 4 √ 2, so 2A & sup2 / / C = 8 √ 2. So the distance from P to the left quasilinear is 4 √ 2 + 8 √ 2 = 12 √ 2 Choose C
- 14. If the distance from a point P on the hyperbola x264 − y236 = 1 to its right focus is 8, then the distance from point P to its right collimator is () A. 10B. 3277C. 27D. 325
- 15. If the distance from the point P on the hyperbola x ^ 2 / 64-y ^ 2 / 36 = 1 to the right focus of the hyperbola is 8, then the distance from P to the right collimator is 8___ , P to the left collimator If the distance from the point P on the hyperbola x ^ 2 / 64-y ^ 2 / 36 = 1 to the right focus of the hyperbola is 8, then the distance from P to the right collimator is 8___ What is the distance from P to the left collimator___ .
- 16. The distance from a point on the left support of hyperbola x square / 9-y square / 16 = 1 to the left focus is 7, then the distance from this point to the right focus of hyperbola is 7
- 17. The distance from a point P on the right branch of hyperbola x ^ 2 / 16-y ^ 2 / 9 = 1 to the left quasilinear is 18, then the distance from the point to the right focus is 18
- 18. If point P is on hyperbola & nbsp; x216 & nbsp; − y212 & nbsp; = 1 and its abscissa is the same as that of the right focus of hyperbola, then the distance between point P and the left focus of hyperbola is______ .
- 19. Make a vertical line of X axis through a focus of hyperbola x square / 144-y square / 25 = 1, and calculate the distance from the intersection of the vertical line and hyperbola to the two focuses
- 20. The distance between the intersection point of the vertical line and the hyperbola and the two focal points can be obtained by making the x-axis vertical line between the hyperbola (xsquare) / 144 - (ysquare) / 25 = 1 and the focal point Through a focus of hyperbola (xsquare) / 144 - (ysquare) / 25 = 1, make a vertical line of X axis, and find the distance from the intersection of the vertical line and hyperbola to the two focuses A = 2x root 5, through the point a (- 5,2), the focus is on the X axis, find the standard equation of hyperbola