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math question

W

wonga1127

macrumors 6502
Original poster
Okay, having trouble with this problem.

Show that the equation of the line tangent to the circle x^2 + y^2 = a^2 at the point (X1 , Y1) (thats x sub 1 y sub 1) on the circle is X1(x) + Y1(y) = a^2

Where do I even start?
 
Oh, my. I should know how to do this...



but I've forgotten, sorry.

Someone here is bound to be able to help
 
the slope from the center (0,0) to the point of tangency (x1,y1) is equal to y1/x1. the line from the center to the point of tangency is perpendicular to the tangent line, so the slope of the tangent line is equal to the negative reciprocal, or -x1/y1. using point-slope formula, you get an equation of y - y1 = (-x1/y1)(x - x1).

multiplying and rearranging will lead you to (x1)*x + (y1)*y = (x1)^2 + (y1)^2. looking at the original equation, (x1)^2 + (y1)^2 is equal to a^2, so substituting will get you your equation of (x1)^2 + (y1)^2 = a^2.

you're welcome. 😉
 
siurpeeman said:
the slope from the center (0,0) to the point of tangency (x1,y1) is equal to y1/x1. the line from the center to the point of tangency is perpendicular to the tangent line, so the slope of the tangent line is equal to the negative reciprocal, or -x1/y1. using point-slope formula, you get an equation of y - y1 = (-x1/y1)(x - x1).

multiplying and rearranging will lead you to (x1)*x + (y1)*y = (x1)^2 + (y1)^2. looking at the original equation, (x1)^2 + (y1)^2 is equal to a^2, so substituting will get you your equation of (x1)^2 + (y1)^2 = a^2.

you're welcome. 😉
Click to expand...
seewhatyoudidthereidid.jpg
 
siurpeeman said:
the slope from the center (0,0) to the point of tangency (x1,y1) is equal to y1/x1. the line from the center to the point of tangency is perpendicular to the tangent line, so the slope of the tangent line is equal to the negative reciprocal, or -x1/y1. using point-slope formula, you get an equation of y - y1 = (-x1/y1)(x - x1).

multiplying and rearranging will lead you to (x1)*x + (y1)*y = (x1)^2 + (y1)^2. looking at the original equation, (x1)^2 + (y1)^2 is equal to a^2, so substituting will get you your equation of (x1)^2 + (y1)^2 = a^2.

you're welcome. 😉
Click to expand...
thank you.

And the lolcat made me laugh.

edit: okay i did the point slop formula and everything, but when I simplfied and rearranged I got y1y + x1x = x1^2 + y1^2. x^2 +y^2 = a^2. im stuck!
 
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