04.042002

# Consider the circle of radius 5 centered at (0,0). Find an equation of the line tangent to the circle at point (3,4). The book gives me the answer: y=-3/4(x-3) but can you explain to me how you get this answer?

keshia
Mathematics
1 3

Consider the circle of radius 5 centered at (0,0). Find an equation of the line tangent to the circle at point (3,4). The book gives me the answer: y=-3/4(x-3) but can you explain to me how you get this answer?

equation of the circle: x² + y² = 25 9 + 16 = 25 => the point (3,5) is on the circle. the line tangent to the circle is perpendicular to the radius O point slope of the radius: 4/3 => slope of the tangent = -3/4 tangent contain (3,4) and have -3/4 as slope. so equation is : y - 4 = -3/4 (x - 3) => y = -3/4x - 4 + 9/4 + 4 => y = -3/4x + 9/4 or y = -3/4(x-3)