Monday

April 21, 2014

April 21, 2014

Posted by **geometry** on Monday, January 24, 2011 at 2:18am.

- gggg -
**Reiny**, Monday, January 24, 2011 at 8:45amTo be a "distance of √10 units away from (3,2) means it has to be tangent to the circle

(x-3)^2 + (y-2)^2 = 10

or

x^2 + y^2 -6x - 4y = -3

let the point of contact be (a,b)

then

a^2 + b^2 - 6a - 4b = -3 (#1)

by slopes...

slope of radius to (a,b) = (b-2)/(a-3)

slope from (a,b) to (8,-3) = (b+3)/(a-8)

but these two lines are perpendicular, so ...

(b+3)/(a-8) = - (a-3)/(b-2)

which simplifies to

a^2 + b^2 - 11a + b = -18 ,(#2)

subtract #1 - #2

5a - 5b = 15

a - b = 3

a = b+3 (#3)

sub #3 into #2 to get it simplified to

b^2 - 2b - 3 = 0

(b-3)(b+1) = 0

b = 3 or b = -1

in #3

a= 6 or a = 2

so (a,b) is either (6,3) or (2,-1)

Now it is easy to find the equation of the two tangents.

Let me know what you got.

**Related Questions**

AP Calc. - find the equation of the tangent line to f(x)=square root x passing ...

Calculus - Determine the equation of the line described by the given information...

Algebra - Use the quadratic formula to solve the equation. Give exact answers: ...

Algebra... - Write the equation of a vertical line passing through the point (8...

math - can someone help me write the equation of the line 1. parallel to the ...

Math ~CHECK MY ANSWER~ - 1) Which of these is a rational number? a. Pi b. Square...

Pre- Algebra - Given an equation of a line, how do I find equations for lines ...

Algebra - Can someone check my answers? 1. Write the equation of the line that ...

Math - Using the distance formula I have to prove that ABC are colinear. A(-1, -...

Algebra - Rationalize each expression by building perfect nth root factors for ...