Find the 5

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


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


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

We would be very happy if you find an error in the example, spelling mistakes, or inaccuracies, and please send it to us. We thank you!

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

2 years ago  2 Likes

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.

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

Next similar math problems:

  • Equation of circle
    circle_analytics find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
  • Circle - AG
    circle2 Find the coordinates of circle and its diameter if its equation is: ?
  • Vector 7
    vectors_sum0_1 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
  • Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  • 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. ..
  • Thunderstorm
    blesk The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tria
  • RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
  • Sphere cuts
    sphere_cut At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
  • Circle
    talesova On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.
  • Triangle IRT
    triangles_5 In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
  • A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  • A cell tower
    tower A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal?
  • Segment
    segment_AB Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
  • Unit vector 2D
    one_1 Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
  • 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.
  • Triangle P2
    1right_triangle Can triangle have two right angles?
  • Inscribed rectangle
    rectangle_inside_circle What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long? Answer: 14 dm