steev

posted by .

can u help
this the qustion is :

A circle passes through the points (1,4)&(5,0) and its centre lies on the line x+y-3=0.Find
(i) the equation of the circle and it parametric equations .
(ii) the centre,diameter and area of the circle .
(iii) the equation of the tangent at (1,4) .
(iv) the equation of the circle concentric with the above circle and passing through the point (7,8).

  • algebra -

    The center of the circle also lies on the perpendicular bisector of any chord. We have the chord between the two given points.
    The chord has slope (0-4)/(5-1) = -1.
    The midpoint of the chord is (3,2).
    The equation of the line containing (3,2) and perpendicular to the chord is

    (y-2)/(x-3) = 1
    or
    -x + y = -1
    This intersects the line
    x + y = 3 at
    (2,1)

    So, our circle has equation

    (x-2)^2 + (y-1)^2 = r^2
    plug in either of the given points and we find r^2 = 10. so,

    (x-2)^2 + (y-1)^2 = 10
    x = 2 + √10 cos t
    y = 1 + √10 sin t

    the rest should be easy to figure out.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. maths

    1) Circle centre (7,-2) passes through (-2,10). Calculate radius and find equation of circle. 2) AB is diameter of circle A(9,5) B(-1,-7). Find equation of circle mid point. I know i have to use the eqn (x1+x2)/2 and (y1+y2)/2 3) Find …
  2. Geometry

    Within an orthonormal system consider points A(1,4) B(5,1) C(4,8) (a)Calculate the angle ABC (b)Show that 3x+4y-19=0 is an equation for line L which passes through A and B (c)Find a vector equation for line L (d)(i)give an equation …
  3. math

    The equation of a circle with centre O(0,0) is x^2+y^2=40. The points A(-2,6) and B(-6,-2) are endpoints of chord AB. DE right bisects chord AB at F. a)Verify that the centre of the circle lies on the right bisector of chord AB. b)Find …
  4. math

    can u help this the qustion is : A circle passes through the points (1,4)&(5,0) and its centre lies on the line x+y-3=0.Find (i) the equation of the circle and it parametric equations . (ii) the centre,diameter and area of the circle …
  5. mathematics

    The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2.1.1 equation of new circle which is the rotation of original circle through 180 degree around the origin...2.1.2 find equation of another circle which is the translation …
  6. math

    Find the centre of the circle that passes through the points p(-9,5), q(1,5), and r(-2,-2)
  7. Math

    find the equation of the circle whose centre lies on the line 5x-2y=9 and the circle touches both the positive axes
  8. math

    ) A chord AB of length 13cm is drawn in a circle centre O at a distance of 5cm from O. Find the radius of the circle. Stop at 1 d.p.(b) TA and TB are tangents to a circle centre O. TOC is a straight line and <ATB = 56°. Calculate …
  9. maths

    the centre of a circle is (2x-1,3x+1). find the x if the circle is passes thuthe centre of a circle is (2x-1,3x+1). find the x if the circle is passes through (-3, -1) and the length of its diameter is 20 units.gh (ro-3, -1) and the …
  10. MATHS

    Q) Find the coordinates of the centre of a circle that passes through points (7,2), (2,3), and (-4,-1)

More Similar Questions