A circle has centre c(5,-4) and it touches the y axis at the point D. The circle cuts the x axis at the points A and B. The tangent at B cuts the y axis at P.
===> determine: the coordinates of the points A and B at which the circle cuts the x-axis..
===> determine: the equation of the tangent at B
===> determine: the coordinates of P.
b)Show by calculation that PD=PB
Feb 9th 2011, 06:07 PM
If the circle just "touches" the x-axis, you know that the radius of said circle will be 5. From that, you should be able to calculate A and B (use the standard form of a circle, and set y to 0). Remember that a tangent is perpendicular to the line that forms from the center of the circle to the point of tangency. Find the line perpendicular to that radius, and find where it intersects the y-axis.