Circle

The circle touches two parallel lines p and q, and its center lies on line a, which is the secant of lines p and q.

Write the equation of the 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:

x_S =  -4.5
y_S =  -8.88
r =  NAN

Solution:

$$\begin{gathered} A=p\cap a=[10;0] \\ B=q\cap a=[-19;0] \\ S={\displaystyle \frac{AB}{2}}=[-4.5;-8.88] \\ t\perp p;t\perp q;S\in t \\ t:+y+1=0 \\ T=p\cap t=[10;NAN] \end{gathered}$$

$y_S=(23.75+(-41.5))\mathrm{/}2=-{\displaystyle \frac{71}{8}}=-8.88$

$$\begin{gathered} r=\mathrm{\mid }SA\mathrm{\mid }=\sqrt{(x_S-x_T{)}^2+(y_S-y_T{)}^2}=NAN \\ (x+4.5{)}^2+(x+8.88{)}^2=NA{N}^2 \end{gathered}$$

Try another example

Showing 1 comment:

Math student

Many examples required

3 years ago  Like

Next similar math problems:

• Isosceles triangle
  In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
• Touch x-axis
  Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
• Prove
  Prove that k1 and k2 is 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
• Circle
  Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
• Three parallels
  The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
• Coordinates
  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
• Find parameters
  Find parameters of the circle in the plane - coordinates of center and radius: ?
• A bridge
  A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water.
• Ellipse
  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.
• Sphere from tree points
  Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
• Two chords
  Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
• MO SK/CZ Z9–I–3
  John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
• Equation of circle 2
  Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
• Find the 5
  Find the equation of the circle with center at (1,20), which touches the line 8x+5y-19=0
• Points on circle
  In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are
• Suppose
  Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
• On a line
  On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].