Friday

August 1, 2014

August 1, 2014

Posted by **Lance** on Monday, January 7, 2013 at 1:51pm.

This problem is confusing? How do I solve this? Please I need your Help

- geometry -
**Steve**, Monday, January 7, 2013 at 3:13pmall points 2√5 from (5,7) form a circle:

(x-5)^2 + (y-7)^2 = 20

Now you want a tangent to the circle that passes through (-5,-3). Must be a tangent, because any other line through the circle will come closer than 2√5 to the center.

So, since lines through (-5,-3) with slope m are

(y+3) = m(x+5), we need

(x-5)^2 + (m(x+5)-3-7)^2 = 20

(x-5)^2 + (mx+(5m-10))^2 = 20

(m^2+1)x^2 + 10m(m-3)x + (5m-10)^2 - 20 = 0

Now for the line to be tangent, the above equation must have a single root. That is, the discriminant must be zero:

100m^2(m-3)^2 - 4(m^2+1)((5m-10)^2-20) = 0

m = 1/2, 2

so, the two lines are

y = 1/2 (x+5) - 3

y = 2(x+5) - 3

**Related Questions**

Math,Geometry - What are the equations of the lines through (-5,-3) and passing ...

Math,Geometry - What are the equations of the lines through (-5,-3) and passing ...

Calculus - Determine the equations of the following lines: (a) having slope ¡1 ...

Analytic Geometry - Find the equation of a circle passing through (3,7) and ...

Analytic Geometry - Find the equation of a circle passing through (-1,6) and ...

Geometry :( - this maths problem is wrecking my head.... 1.find the points of ...

Precalculus check answers help! - 16. Find the distance between P (–2, 5) and ...

Precalculus check answers help! - 16. Find the distance between P (–2, 5) and ...

Analytic Geometry - Find the equation of a circle passing through (3,7) and ...

Geometry - Okay, this is a problem that I've tried over ten times before getting...