Circle

Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q.

Write the equation of circle and determine the coordinates of the center and radius.

p: x-10 = 0
q: -x-19 = 0
a: 9x-4y+5 = 0


Correct result:

xS =  -4.5
yS =  -8.88
r =  NAN

Solution:

A=pa=[10;0] B=qa=[19;0] S=AB2=[4.5;8.88] tp;tq;St t:+y+1=0 T=pt=[10;NAN] A = p \cap a = [10; 0] \ \\ B = q \cap a = [-19; 0] \ \\ S = \dfrac{ AB }{2} = [-4.5; -8.88] \ \\ t \perp p ; t \perp q; S \in t \ \\ t: +y +1 = 0 \ \\ T = p \cap t = [10; NAN] \ \\
yS=(23.75+(41.5))/2=718=8.88y_{ S }=(23.75+(-41.5))/2=- \dfrac{ 71 }{ 8 }=-8.88
r=SA=(xSxT)2+(ySyT)2=NAN  (x+4.5)2+(x+8.88)2=NAN2 r = |SA| = \sqrt{ (x_S-x_T)^2+(y_S-y_T)^2 } = NAN \ \\ \ \\ (x +4.5)^2+(x +8.88)^2 = NAN^2 \ \\



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!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 1 comment:
#
Math student
Many examples required

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.
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.

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

Next similar math problems:

  • 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
  • In the
    rectangle_1 In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm2.
  • Coordinates
    geodet Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
  • The circumference
    rectangle The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
  • The tower
    veza_huly The observer sees the base of the tower 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
  • Summands
    numbers_2 We want to split the number 110 into three summands so that the first and the second summand are in the ratio 4: 5, and the third with the first are in ratio 7: 3. Calculate the smallest of the summands.
  • Lookout tower
    tower How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now.
  • A bottle
    flasa A bottle full of cola weighs 1,320 g. If we drink three-tenths of it, it will weigh 1,008g. How much does an empty bottle weigh?
  • Water mixing
    watermixing We have 520 ml of hot water and 640 ml of water at 48°C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65°C?
  • Columns of two and three
    skola_2 When students in one class stand in columns of two there is none left. When he stands in columns of three, there is one student left. There are 5 more double columns than three columns. How many students are in the class?
  • Side lengths
    triangles_1 In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
  • Adam
    minca Adam has half the money in his right pocket than in his left pocket. If he transferred 40 crowns from the left pocket to the right, he would have the same in both pockets. Calculate how many crowns does Adam have in his left pocket more than in his right?
  • Wire fence
    plot_zed The wire fence around the garden is 160 m long. One side of the garden is three times longer than the other. How many meters do the individual sides of the garden measure?
  • The four
    mince_2 The four pirates divided 65 coins to each other. They were sorted by age, the youngest receiving the least number of coins, each half more than the previous one. How many coins did the oldest pirate receive?
  • In a
    triangles_1 In a triangle, the aspect ratio a: c is 3: 2 and a: b is 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
  • Students
    penize Students Aleš, Bohouš, Cyril, and Dušan were on a brigade. They divided the total revenue as follows: Aleš received two-fifths of the revenue, Bohouš received one-sixth of the revenue, Cyril received three-tenths of the revenue, and Dušan received the res
  • Working together
    workers Two people will do the work in 12 days. They worked together for 8 days. Then only one worked for 10 days. How many days would each of them do the work if he worked alone?