Find the 5

Find the equation with center at (1,20) which touches the line 8x+5y-19=0

Result

e = (Correct answer is: e = pow(x-1, 2)+pow(y-20, 2) = 89) Wrong answer

Solution:

x0=1 y0=20  8x+5y19=0  s=8 x0+5 y019=8 1+5 2019=89 a=82+52=899.434 r=sa=899.434899.434  (xx0)2+(yy0)2=r2 e=(x1)2+(y20)2=89x_{0}=1 \ \\ y_{0}=20 \ \\ \ \\ 8x+5y-19=0 \ \\ \ \\ s=8 \cdot \ x_{0}+5 \cdot \ y_{0}-19=8 \cdot \ 1+5 \cdot \ 20-19=89 \ \\ a=\sqrt{ 8^2+5^2 }=\sqrt{ 89 } \doteq 9.434 \ \\ r=\dfrac{ s }{ a }=\dfrac{ 89 }{ 9.434 } \doteq \sqrt{ 89 } \doteq 9.434 \ \\ \ \\ (x-x_{0})^2 + (y-y_{0})^2=r^2 \ \\ e=(x-1)^2+(y-20)^2=89



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 1 comment:
#
Dr Math
Hint - use formula for Distance Between a Point and a Line = which is radius of circle

1 year ago  2 Likes
avatar









Tips to related online calculators
For Basic calculations in analytic geometry is 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.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 

 

Next similar math problems:

  1. 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
  2. Vector perpendicular
    3dperpendicular Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
  3. 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?
  4. Coordinates of square vertices
    ctverec_2 The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.
  5. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
  6. 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?
  7. Line
    negative_slope Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
  8. Three points 2
    vectors_sum0 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
  9. 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. ..
  10. Vector equation
    collinear2 Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent
  11. Cuboids
    3dvectors Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
  12. Coordinates of a centroind
    triangle_234 Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
  13. Decide 2
    vectors2 Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line
  14. Set of coordinates
    axes2 Consider the following ordered pairs that represent a relation. {(–4, –7), (0, 6), (5, –3), (5, 2)} What can be concluded of the domain and range for this relation?
  15. Two people
    crossing Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa
  16. Points collinear
    collinear Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
  17. Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.