Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].


h = (Correct answer is: ) OK


x0=0+02=0 y0=4 6+(4) 62=0  S[0,0] xx0a2yy0b2=1 xa2yb2=1  c=a2+b2 h=30a224b2=1x_{0}=\dfrac{ 0+0 }{ 2 }=0 \ \\ y_{0}=\dfrac{ 4 \cdot \ \sqrt{ 6 }+(-4) \cdot \ \sqrt{ 6 } }{ 2 }=0 \ \\ \ \\ S[0,0] \ \\ \dfrac{ x-x_{0} }{ a } ^2-\dfrac{ y-y_{0} }{ b } ^2=1 \ \\ \dfrac{ x }{ a } ^2-\dfrac{ y }{ b } ^2=1 \ \\ \ \\ c=\sqrt{ a^2+b^2 } \ \\ h=\dfrac{ 30 }{ a } ^2-\dfrac{ 24 }{ b } ^2=1

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Showing 0 comments:

Tips to related online calculators
Looking for help with calculating arithmetic mean?
For Basic calculations in analytic geometry is a helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Looking for a statistical calculator?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Next similar math problems:

  • Sphere equation
    sphere2 Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
  • Find the 3
    segment_2 Find the distance and midpoint between A(1,2) and B(5,5).
  • Hyperbola equation
    hyperbola_4 Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
  • On line
    primka On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
  • Vertex points
    PQR_triangle Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area.
  • Vertices of a right triangle
    right_triangle_5 Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
  • Prove
    two_circles_1 Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
  • Vertices of RT
    RightTriangleMidpoint_3 Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
  • Distance between 2 points
    axes2 Find the distance between the points (7, -9), (-1, -9)
  • Three points
    abs1_1 Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
  • Touch x-axis
    touch_circle Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
  • Medians and sides
    taznice3 Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
  • Circle
    circle_ag Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
  • Right triangle from axes
    axes2 A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
  • Is right-angled
    rt_sqrt_2 Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 and √8) be a right triangle?
  • Distance problem
    linear_eq_3 A=(x, x) B=(1,4) Distance AB=√5, find x;
  • Right angled triangle 2
    vertex_triangle_right LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n