SOLUTION: The equation of the tangent line to the curve x^2 + y^2 =169 at the point (5,-12) is (A) 5y-12x= -120 (B) 5x-12y= 119 (C) 5x-12y= 169 (D) 12x+5y= 0 (E) 12x+5y= 169

Question 243003: The equation of the tangent line to the curve x^2 + y^2 =169 at the point (5,-12) is
(A) 5y-12x= -120
(B) 5x-12y= 119
(C) 5x-12y= 169
(D) 12x+5y= 0
(E) 12x+5y= 169
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First derive both sides of

with respect to 'x' to get

Now solve for y':

So the slope is simply the negative quotient of the two coordinates. For the point (5,-12), the slope at that point is (since and )

-----------------------------------------------------

Now recall that the point slope formula is

where 'm' is the slope and

is the point in which the line goes through.

Plug in , , and

Rewrite as

Distribute

Multiply and to get

Subtract 12 from both sides to isolate y

Combine like terms and to get

Multiply EVERY term by the LCD 12 to clear out the fractions.

Subtract 5x from both sides.

Multiply EVERY term by -1 to make the 'x' coefficient positive.

So the equation of the tangent line is
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