Question

Find the equation of the tangent to the circle x²+y²=169 at the point (5,12)

Answer 1

12y + 5x = 169

Explanation:

Slope of the normal:

(12-0)/(5-0)

12/5

Slope of the tangent

-5/12

y - 12 = (-5/12)(x - 5)

12y - 144 = -5x + 25

12y + 5x = 169

Answer 2

Explanation:

hello :

use equation for this circle : the center is : O(0,0)

the radius is 13

let (∆) this tangent in A(5,12) where an equation is : y-y1 = m(x-x1)

x1 = 5 and y1 =12 calculate : m the slope of this tangent

but (∆) tangent in A(5,12) for this circle : means the line (OA)⊥tangent(∆)

the slope of (OA)×m = -1

but the slope of (OA)= (12-0)/(5-0)=12/5

(12/5)×m =-1 so : m=-5/12

an equation for this tangent is y-12 = (-5/12)(x-5)