Question

You are given the circle, x2 + y2 = 25.

Find the equation of the tangent line to the circle at Point B.
Point B = (4,3)

Answer 1

find slope by getting the first derivative of the function... then use point-slope form for the equation of tangent line...

Answer 2

\[x^2+y^2=25\]\[2x~dx+2y~dy=0\]\[\bcancel2y~dy=-\bcancel2x~dx\]\[\frac{dy}{dx}=-\frac{x}{y}=m\]just plug-in [4,3] to find slope of a line...

Answer 3

so that would give me -4/3..?

Answer 4

then use point-slope formula of a line:\[(y-y_1)=m(x-x_1)\]where \([x_1,y_1]\) is also [4,3] point which is the tangent point between the circle and the line...

Answer 5

y-3=-4/3(x-4) would be the equation of the line tangent then..

Answer 6

yup it's negative 'cause its inclined to the left...

Answer 7

yes just simplify your equation...

Answer 8

okay so it would be -4/3x+25/3..? idk if i did my math wrong but it said it was wrong ;/

Answer 9

oh nvm! I typed it in with a different variable. Thank you so much!!!

Answer 10

it should be... \[3y-9=-4x+16\]\[3y+4x=16+9=25\]\[4x+3y=25\]

Answer 11

no problem...