Gradient of circle?

posted by .

A circle has the equation x^2+y^2-4x+6y-12=0
and i have already found that the centre has a coordinate of (2,-3), and a radius of 5 units. But i need to find points on the circle that has the gradient of -4/3 when a tangent is drawn on the point. How do i do that???

  • Gradient of circle? -

    Assuming you have not done Calculus, we will work without it.
    Let O = centre point of the circle
    If the tangent to the point P has a gradient of m, what can you say about the gradient (slope) of the radius OP, denoted by p?
    We know that OP and the tangent are perpendicular to each other, so m*p=-1.
    You can therefore find p knowing m.
    What is the line passing through the centre (2,-3) with a slope of p?
    (y-(-3)) = p(x-2)
    The intersection of this line with the circle will give you the required tangent points. Note that there are two such points. It will be the solution of a quadratic equation.

  • Gradient of circle? -

    I see! Thanks!

  • Gradient of circle? :) -

    You're welcome!

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. Pre-Calc (Circles)

    Describe the conditions necessary, where circle A has a larger radius than circle B, for the two circle to have no points of intersection, while circle B is entirely in the interior of circle A.
  3. steev

    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 …
  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. 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 …
  7. 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 …
  8. 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 …
  9. Geometry midpoint formula

    A circle on the Coordinate plane has a diameter with endpoints at (6,8) and (15,8). What are the coordinates of the center of the circle?
  10. Maths

    1. In the xy-coordinate plane, point A is the midpoint of the segment with endpoints (2,4) and (-4,-4). What is the distance from point A to the origin?

More Similar Questions