Posted by Lance on Monday, January 7, 2013 at 4:57pm.
Make a sketch, let the point of contact be P(x,y)
(there will be two of them, let the math take care of it)
label A(-5,-3) and B(5,7)
point P must be on a circle with centre B(7,5) and radius of BP = 2√5
the equation of that circle is
(x-7)^2 + (y-5)^2 = 20
which when expanded gets us
x^2 + y^2 = 10x+14y-54
also the slope of AP must be the negative reciprocal of the slope of BP
slope AP = (y+3)/(x+5)
slope BP = (y-7)/(x-5)
then (x-5)/-(y-7) = (x+5)/(y+3)
x^2 - 25 = -y^2 + 7y + 21 - 3y
x^2 + y^2 = 4y + 46
So 10x + 14y - 54 = 4y+46
10x = -10y + 100
x = 10- y
Then in x^2 + y^2 = 4y + 46
(10-y)^2 + y^2 = 4y + 46
100 - 20y + y^2 + y^2 = 4y + 46
2y^2 - 24y + 54 = 0
y^2 - 12y + 27 = 0
(y-3)(y-9)= 0
y = 3 or y = 9
if y = 3, then x = 10-3 = 7 ...... P is (7,3)
if y = 9, then x = 10-9 = 1 ...... P is (1,9)
almost done ......
for P as (7,3)
slope of AP = (3+3)/(7+5) = 6/12 = 1/2
equation of AP:
y+3 = (1/2)(x+5)
2y + 6 = x+5
x - 2y = 1 is one of the line equations
for P as (1,9)
.......
I will let you have the pleasure of finishing it.
(check my work, but it came out so nice to have an error in it)
Related Questions
Math,Geometry - What are the equations of the lines through (-5,-3) and passing ...
geometry - What are the equations of the lines through (-5, -3) and passing at ...
Calculus - Determine the equations of the following lines: (a) having slope &...
Precalculus check answers help! - 16. Find the distance between P (–2, 5) ...
Precalculus check answers help! - 16. Find the distance between P (–2, 5) ...
Algebra - Can someone check my answers? 1. Write the equation of the line that ...
Vectors - I am really lost and confused! Consider the lines r = (1,-1,1) + t(3,2...
Math - Find two lines passing through (-1, 1)which are tangent to the ellipse x^...
Algebra - Write a system of inequalities to express the exterior of the triangle...
gggg - what are the equation of a line through (8,-3) and passing distance ...
For Further Reading
