Hiii im new here and i really need some answers huhuhu :((
How can you find the equation of a tangent if there is no given point?? Our teacher gave us an item to solve about equation of a tangent and she gave us
x^2+y^2+6x-10y+17=0
I hope you can help meeeee :(
+129842 This is the graph of a circle.......if you have had calculus, we can use implcit differentiation to find the slope of a line that is tangent to the circle at any point (x, y)......this is given by :
x^2+y^2+6x-10y+17=0 implicitly differentiate
2x + 2yy' + 6 -10y' + 0 = 0
y' [ 2y -10 ] = - [ 2x + 6] divide through by 2
y' [ y - 5] = - [ x + 3] divide by [ y - 5]
y' = - [ x + 3] / [ y -5] factor out a -1
y' = [ x + 3] / [5 - y] the right side is the slope of the tangent line for any (x , y) on the circle.....so......you can use this slope and the point to write an equation for a tangent line just like you would in Algebra !!!........note that the slope is undefined when y = 5
