What is the length of the radius of a circle with center (10, -14) that is tangent to the line x=13?

The length of the radius of a circle as described in the question is; 14.32

The center of the circle is at; (10, -14)

The line that is tangent to the circle is; x = 13.

The coordinate of a point on the line is therefore; (13, 0)

The length of the radius of the circle can.be obtained from Pythagoras theorem as;

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length of radius of a circle = 3

Step-by-step explanation:

a tangent line touches the circle at one point

if the tangent line is at x=13 (vertical line) and the center of the circle is

(x,y) = (10,-14) with its center x at 10; then take the difference to find the radius;

x(tangent line) - x(center of circle) = radius of circle

length of radius of a circle = 13-10 = 3

you can also graph the circle and draw the tangent line to find the radius

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation:

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)