calculus

posted by .

conic sections

question 1:
verify that the point (3,2) lies on the circle x^2+y^2-8x+2y+7=0, and find the equation of the tangent at this point.

question 2:
find the length of the tangents from the point (5,7) to the circle x^2+y^2-4x-6y+9=0

question 3:
find the equation of the common chord of the circles x^2+y^2-6x+2y+1=0 and x^2+y^2+4x-2y-13=0

  • calculus -

    #1. Have you tried plugging x=3 and y=2 into the equation? Do it and verify that the equation is satisfied there.
    Then get the circle's slope dy/dx at (3,2) by implicit differentiation.
    Once you know one point on the line (3,2), and the slope at that point, the equation of the line can easily be written.
    (y-2) = (x-3)*dy/dx

    #2 Rewrite the circle equation
    (x-2)^2 -4 + (y-3)^2 -9 + 9 = 0
    (x-2)^2 + (y-3)^2 = 4
    That tells you the circle's center location and radius. Plot it and the point (5,7) on a graph. Draw a line from (5,7) to the circle's center at (2,3). From the length of that line (a hypotenuse) and the radius of the circle, use the Pythagorean theorem to get the length of the tangent. A tangents, radius to the tangency point, and hypotenuse form a right triangle.

    3. That's all I have time for. Please show your own work on future posts

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Conic sections A circle passes through points A(-5,2), B(-3,-4) and C(1,8). Find the coordinate of the point of intersection of the perpendicular bisectors of AB and BC. What is the equation of the circle?
  2. Calculus

    Conic Sections- A point moves so that its distance from the origin is twice its distance from the point (3,0). Show that the locus is a circle, and find its centre and radius.
  3. Calculus - Maths

    I got a few questions. Hope ya'll can help out. 1) for F(X) = 6x - 2x^2 Find the gradient of the chord joining the point where the X coorinates are 1 and (1+h) respectively. b) hence find the gradient at x=1 2) Find the Coordinates …
  4. Calculus - Damon

    Find the line which passes through the point (0, 1/4) and is tangent to the curve y=x^3 at some point. So I found the derivative which is 3x^2. Let (a, a3) be the point of tangency. 3x^2 = (a3 - 1/4)/(a-0) I'm not sure how to solve …
  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. Math

    The point P = (4, 3) lies on the circle x2 + y2 = 25. Find an equation for the line that is tangent to the circle at P. This line meets the x-axis at a point Q. Find an equation for the other line through Q that is tangent to the circle, …
  10. Math

    The point P = (4, 3) lies on the circle x2 + y2 = 25. Find an equation for the line that is tangent to the circle at P. This line meets the x-axis at a point Q. Find an equation for the other line through Q that is tangent to the circle, …

More Similar Questions