Circle O's center is at (1,5) and has a radius of the square root of 34.
Line AB is tangent to this circle at (6,2). Find the equation of this line.
2007-05-12 11:21:08 · 8 answers · asked by 2 days after my B day :) 2 in Science & Mathematics ➔ Mathematics
A tangent to a circle is perpendicular to the radius drawn to the point of tangency.
First, locate the center of the circle. In this case is it (1, 5).
Find the slope of the radius
Using (6, 2) and (1, 5) .. the slope of the radius is 3/-5
Take the opposite reciprocal to find the slope of a line perpendicular ... so the slope of the line is 5/3
The equation of the line is (y - 2) / (x - 6) = 5/3
To put it in standard form cross multiply
5x - 30 = 3y - 6
5x - 3y = 24
Solve for y if you need an equation in slope-intercept form
y = (5/3)x - 8
2007-05-12 11:26:43 · answer #1 · answered by suesysgoddess 6 · 2⤊ 0⤋
Where are you having trouble? It looks like you've simply handed us your homework -- doing it is your job, but we'll help you get over a rough spot.
You already know a critical radius: running from (1,5) to the tangent point at (6,2). What is the angle between a tangent and a radius at the point of tangency? How do you find the tangent's slope from the slop of the radius?
Answer those, grind some numbers, and you should be able to find the answer.
2007-05-12 11:32:49 · answer #2 · answered by norcekri 7 · 0⤊ 1⤋
The equation of the circle is:
(x - 1)^2 + (y - 5)^2 = 34
(y - 5)^2 = 34 - (x - 1)^2.
2(y - 5)(dy/dx) = -2(x - 1)
dy/dx = -(x - 1) / (y - 5)
When x = 6 and y = 2, the gradient is 5 / 3.
The tangent is therefore:
y = (5/3)x + c ...........(1)
and c must satisfy:
2 = (5/3)6 + c ..........(2)
Substituting for c from (2) in (1):
y = (5/3)x - 8.
2007-05-12 11:35:57 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Eqn of circle is (x-1)^2+(y-5)^2= 34
differentiate both sides with respects to x.
2(x-1)+(dy/dx)(2)(y-5)=0
dy/dx= -(x-1)/(y-5)
At (6,2),
dy/dx=-(6-1)/2-5)
=5/3
gradient of tangent = 5/3
equation ----> y= 5/3x+c
At (6,2)
2=(5/3)(6)+c
c=-8
Therefore, equation is y=-5/3x-8
2007-05-12 11:28:54 · answer #4 · answered by Michael Toh 3 · 0⤊ 1⤋
Slope intercept for is: y = mx + b for the reason which you have each and every of the values different than b you could fill in and resolve for b. y = mx + b -5 = (4/5)(0) + b -5 = 0 + b b = -5 So, y = (4/5)x - 5
2016-12-17 11:00:16 · answer #5 · answered by ? 4 · 0⤊ 0⤋
You need to do your own homework.
2007-05-12 11:23:59 · answer #6 · answered by Alice K 7 · 0⤊ 1⤋
use point slope form :
y - y1 = m(x - x1) +b
2007-05-12 11:25:16 · answer #7 · answered by mattman059 2 · 0⤊ 1⤋
02851034104...did I win?
2007-05-12 11:24:24 · answer #8 · answered by Anonymous · 0⤊ 1⤋