Monday

November 24, 2014

November 24, 2014

Posted by **Allen** on Thursday, October 22, 2009 at 11:17pm.

r^2(1 + m^2) = b^2

Hint:

The quadratic equation x^2 + (mx + b)^2 = r^2 has exactly one solution.

- Alg2 -
**Reiny**, Thursday, October 22, 2009 at 11:35pmsub y = mx + b into x^2 + y^2 = r^2

expanding gave me

x^2 + m^2x^2 + 2bmx + b^2 - r^2 = 0

a^2(1+m^2) + 2bmx + b^2 - r^2 = 0

comparing this to Ax + By + C = 0

A = 1+m^2

B = 2bm

C = b^2 - r^2

we want this quadratic to have only one solution, since there is only one point of contact.

(That was the given hint)

So the discriminant of the quadratic formula must be zero, B^2 - 4AC = 0

(2bm)^2 - 4(1+m^2)(b^2 - r^2) = 0

4b^2m^2 - 4(1+m^2)(b^2 - r^2) = 0

b^2m^2 - (1+m^2)(b^2 - r^2) = 0

b^2m^2 - b^2 + r^2 - b^2m^2 + r^2m^2 = 0

- b^2 + r^2 + r^2m^2 = 0

r^2(1 + m^2) = b^2

as requested.

**Answer this Question**

**Related Questions**

Math (Pre Cal) - Hi, I am studying for a precalculus quiz and I do not ...

math - From an exteror point P that is h units form a circle of radius r, a ...

homework check - which if the following statements is false? a. The points of a ...

Math - From an exterior point P that is h units from a circle of radius r, a ...

mathematics - The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2....

mathematics - The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2....

mathematics - The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2....

Math - Circle C has radius 4 inches. Circle D had radius 9 inches. These two ...

mathematics - The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2....

Math - Answer check please: Consider the circle (x-3)^2 + (y+1)^2 = 169. The ...