Tangents to ellipse

Find the magnitude of the angle at which the ellipse x2 + 5 y2 = 5 is visible from the point P[5, 1] .

Correct result:

A =  26.5651 °

Solution:

x2+5 y2=5 P0=5;P1=1  x2/5+(y/1)2=1 a=5=52.2361 b=1 x0=0 y0=0  p1,p2:y=kx+q b2q2+a2 k2=0  1q2+5 k2=0 P1=k P0+q  1(P1kP0)2+5k2=0  1(1k 5)2+5 k2=0 20k2+10k=0 20k210k=0  a=20;b=10;c=0 D=b24ac=1024200=100 D>0  k1,2=b±D2a=10±10040 k1,2=10±1040 k1,2=0.25±0.25 k1=0.5 k2=0   Factored form of the equation:  20(k0.5)k=0   q1=P1k1 P0=10.5 5=32=1.5 q2=P1k2 P0=10 5=1  φ1=180πarctan(k1)=180πarctan(0.5)26.5651 φ2=180πarctan(k2)=180πarctan(0)=0  A=φ1φ2=26.56510=26.5651=263354"

Our quadratic equation calculator calculates it.




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:
avatar




Tips to related online calculators
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 help with calculating roots of a quadratic equation?
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

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

Next similar math problems:

  • Find the 15
    ellipseTangent Find the tangent line of the ellipse 9 x2 + 16 y2 = 144 that has the slope k = -1
  • Ellipse
    elipsa Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
  • 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].
  • 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
  • Curve and line
    parabol The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
  • Find the 5
    distance-between-point-line Find the equation of the circle with center at (1,20), which touches the line 8x+5y-19=0
  • 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).
  • Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  • The angle of lines
    lines Calculate the angle of two lines y=x-21 and y=-2x+14
  • Power line pole
    pole From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.
  • Find the 10
    lines Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?
  • 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?
  • 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
  • Angle
    atan A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
  • Parametric form
    vzdalenost Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. ..
  • Angle of cone
    kuzel2 The cone has a base diameter of 1.5 m. The angle at the main apex of the axial section is 86°. Calculate the volume of the cone.
  • Intersections 3
    intersect_circles Find the intersections of the circles x2 + y2 + 6 x - 10 y + 9 = 0 and x2 + y2 + 18 x + 4 y + 21 = 0