SOLUTION: Hi! What are the equations of the lines through (8,-3) and passing at distance √10 from (3,2)? I've answered all my homework except this. Please help! Thanks!

Algebra ->  Linear-equations -> SOLUTION: Hi! What are the equations of the lines through (8,-3) and passing at distance √10 from (3,2)? I've answered all my homework except this. Please help! Thanks!      Log On


   

Question 1017503: Hi!
What are the equations of the lines through (8,-3) and passing at distance √10 from (3,2)?
I've answered all my homework except this.
Please help! Thanks!
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hi!
What are the equations of the lines through (8,-3) and passing at distance sqrt%2810%29 from (3,2)?
I've answered all my homework except this.
Please help! Thanks!
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I'd solve this problem in this way: 

1. The equation of a straight line passing through (8,-3) is

   y + 3 = m*(x-8),          (1)

   where m is a parameter, now unknown.


2. The equation of the given circle is 

   %28x-3%29%5E2+%2B+%28y-2%29%5E2 = 10.   (2)


3. Now substitute the expression  y = m*(x-8)-3  from (1) into equation (2) and find the coefficient m 
   under the condition that the obtained quadratic equation has only one real root.

   This requirement means that the straight line is tangent to the circle and, hence, lies at the distance sqrt%2810%29 from its center.

Now my question is: is this advice enough for you?
Can you complete the solution yourself?