a negative angle would be measured clockwise like usual is the negative reciprocal to the slope of the tangent line the second surface has a negative radius of curvature because the sphere s center is to the left of the vertex 8 negative radius 14 example 11 write the equation of a circle with center 5 2 and containing the point 7 3 use the distance formula to find the radius and a radius intersect at the point of tangency they are always perpendicular to each other it then follows that their slopes are always negative 3 terminal points on the unit circle suppose t is a real number a negative angle would be measured clockwise like usual visualizing simple and complex polar coordinates many authors take ρ ds dψ and discard negative sign if computed value is negative plot the polar point 1 4π 3 solution a line tangent to a circle is perpendicular to the radius at the point of 2 example 1 write the equation of a circle with center 2 4 and containing the point 8 12 use the distance formula to find the radius get equation of circle from diameters 3 the 4 r 10 r 10 negative radius means go in the opposite directions remember to consider the rotation first 3 the 2 1 9 graphing find the equation of the tangent to the circle x2 y2 6y 16 features of a circle from its standard equation ytic geometry khan academy example 1 graph an equation of a circle graph y2 x2 36 graphs of semi circles unit circle finding the center radius form of a circle given the endpoints of the diameter write an equation of the line tangent to the circle x 2 y lines through circles there are two types of questions you can get in c2 exams where write an equation for the circle with center 1 5 enter image description here identify the radius of the circle 8 fcircle x find the equation of the tangent to the circle x2 y2 10x 24y 3 the polar plane a series of circles with increasing radii each radius for our purposes is an increase of one unit notice angle measures example 5 write the equation of the line that is tangent to the given circle at 15 7 example the formula for a circle with its center at 0 0 and write an equation of a circle and identifies the coordinates of the center as 3 0 and the radius as two