Intersections 3

Find the intersections of the circles
x2 + y2 + 6 x - 10 y + 9 = 0 and
x2 + y2 + 18 x + 4 y + 21 = 0

Correct result:

x1 =  -1.334
y1 =  0.286
x2 =  -7.914
y2 =  5.926

Solution:

x2+y2+6 x10 y+9=0 x2+y2+18 x+4 y+21=0  e2e1: (186)x+(4+10)y+(219)=0 y=6/7(x+1)   x2+(6/7(x+1))2+6x10(6/7(x+1))+9=0  x2+(6/7(x+1))2+6 x10(6/7(x+1))+9=0 1.734693877551x2+16.041x+18.306=0  a=1.734693877551;b=16.041;c=18.306 D=b24ac=16.041241.73469387755118.306=130.2857142857 D>0  x1,2=b±D2a=16.04±130.293.469387755102 x1,2=4.62352941±3.2899974232486 x1=1.3335319885161=1.334 x2=7.9135268350134   Factored form of the equation:  1.734693877551(x+1.3335319885161)(x+7.9135268350134)=0x^2 + y^2 + 6 \ x - 10 \ y + 9=0 \ \\ x^2 + y^2 + 18 \ x + 4 \ y + 21=0 \ \\ \ \\ e_{2}-e_{1}: \ \\ (18-6)x + (4+10)y + (21-9)=0 \ \\ y=-6/7 (x + 1) \ \\ \ \\ \ \\ x^2 + (-6/7 (x + 1))^2 + 6 x - 10 (-6/7 (x + 1)) + 9=0 \ \\ \ \\ x^2 + (-6/7 (x + 1))^2 + 6 \ x - 10 (-6/7 (x + 1)) + 9=0 \ \\ 1.734693877551x^2 +16.041x +18.306=0 \ \\ \ \\ a=1.734693877551; b=16.041; c=18.306 \ \\ D=b^2 - 4ac=16.041^2 - 4\cdot 1.734693877551 \cdot 18.306=130.2857142857 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ -16.04 \pm \sqrt{ 130.29 } }{ 3.469387755102 } \ \\ x_{1,2}=-4.62352941 \pm 3.2899974232486 \ \\ x_{1}=-1.3335319885161=-1.334 \ \\ x_{2}=-7.9135268350134 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 1.734693877551 (x +1.3335319885161) (x +7.9135268350134)=0

Checkout calculation with our calculator of quadratic equations.

y1=6/7 (x1+1)=6/7 ((1.3335)+1)=5011750=0.286y_{1}=-6/7 \cdot \ (x_{1} + 1)=-6/7 \cdot \ ((-1.3335) + 1)=\dfrac{ 501 }{ 1750 }=0.286
y2=6/7 (x2+1)=6/7 ((7.9135)+1)=5.926y_{2}=-6/7 \cdot \ (x_{2} + 1)=-6/7 \cdot \ ((-7.9135) + 1)=5.926



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 0 comments:
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 system of equations and looking for calculator system of linear equations?

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

Next similar math problems:

  • 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
  • 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).
  • 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
  • Find the 5
    distance-between-point-line Find the equation with center at (1,20) which touches the line 8x+5y-19=0
  • 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)
  • Vector v4
    scalar_product Find the vector v4 perpendicular to vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1)
  • 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?
  • 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.
  • Dodecagon
    clocks Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
  • 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?
  • 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.
  • 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
  • Calculate 6
    distance_point_line Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].
  • 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 the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  • 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?
  • Decide 2
    vectors2 Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line