the equation of a circle is (x+2)^2+(y-4)^2=25
whats the equation of the tanget (-5,8)?

Question

the equation of a circle is (x+2)^2+(y-4)^2=25
whats the equation of the tanget (-5,8)?

anonymous · Answer

implicit diff for this one 
$$(x+2)^2+(y-4)^2=25$$
$$2(x+2)+2(y-4)y'=0$$
$$y'=\frac{x+2}{y-4}$$ then replace $x$ by -5, $y$ by 8

anonymous · Answer

i dont get your answer satellite

anonymous · Answer

you want the slope of the tangent line right?

anonymous · Answer

yes, but the equation of the slope is |dw:1337306074318:dw|

anonymous · Answer

that is an equation of the slope if you know two points. you only have one point, the point of tangency
so you need the derivative right?

anonymous · Answer

is this calculus class or something else?

anonymous · Answer

reason i ask is because i cannot figure out how to find the slope of the tangent line without using calculus

anonymous · Answer

maybe dpalnc has another method, but i do not

anonymous · Answer

i did the same too... i thought this was a calc problem..  :) it's an alg2 problem, right?

anonymous · Answer

find the slope of the line connecting the center to the point of tangency...
the slope of your tangent line is the negative reciprocal of that slope.

anonymous · Answer

well, im in plain geometry, and i tought you find the slope using the equation of the circle

anonymous · Answer

i did not take calcus yet or algerbra 2 so im stuck

anonymous · Answer

the equation of the circle is already given.  what you need is the center of the circle.

anonymous · Answer

geometry is good here too...

anonymous · Answer

yea, that easy, the center of the circle is (-2, 4)

anonymous · Answer

i dont get how you would find the slope of the tanget from the center of the circle

anonymous · Answer

good.
can you find the slope of the line that connects (-2, 4) with (-5, 8) ?

anonymous · Answer

okk, its the slope from the center to the tanget is -4/3

anonymous · Answer

good..

anonymous · Answer

did you know that a line that is tangent to a circle is ALWAYS perpendicular to the radius at the point of tangency?

anonymous · Answer

yes haha, but from that how do you find the slope of the tanget?

anonymous · Answer

how do perpendicular lines relate in terms of their slope?

anonymous · Answer

i have no idea man that why i need help

anonymous · Answer

that's the key...
perpendicular slopes are negative reciprocals of each other...
so if your slope is -4/3, the slope perpendicular to that is.... what?

anonymous · Answer

ohh! i see, its 3/4!