Friday

March 6, 2015

March 6, 2015

Posted by **Dealie** on Saturday, August 28, 2010 at 11:57pm.

"The tangent line to a circle may be defined as the point that intersects a circle in a single point... If the equation of the circle is x^2+y^2=r^2 and the equation of the tangent line is y=mx+b show that:

a. r^2(1+m^2)=b^2 [Hint: the quadratic equation x^2+(mx+b)^2=r^2 has exactly one solution]

b.the point of tangency is (-r^2m/b,r^2/b)

c. the tangent line is perpendicular to the line containing the circle and the point of tangency

- Math (Pre Cal) -
**drwls**, Sunday, August 29, 2010 at 12:26ama. For the equation

x^2+(mx+b)^2 = r^2

to have one solution, the discriminant of the quadratic equation

Ax^2 + Bx + C = 0

must be zero

B^2 = 4 AC

A = 1+m^2

B = 2mb

C = b^2-r^2

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

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

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

b. x = -B/(2A) = -mb/(1+m^2)

= -mb[r^2/b^2] = -mr^2/b

c. Don't you mean the line containing the CENTER OF the circle and the point of tangency?

- Math (Pre Cal) -
**Dealie**, Sunday, August 29, 2010 at 9:46amThank you so much. you totally rock

**Answer this Question**

**Related Questions**

Alg2 - The tangent to a circle may be defined as the line that intersects the ...

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

Geometry - Suppose that line t is tangent to circle center O and radius OP at ...

Math - P is a point outside of circle Γ. The tangent from P to Γ ...

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....

GEOMETRY INSCRIBED ANGLES MULTIPLE CHOICE QUESTION - segment BC is tangent to ...

math b - how to find if line rp is tangent to circle 0 at p, and the circle ...

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