Find the equation of the tangent line to the ellipse x 2 + 4y 2 = 25 when x = 3 and y < 0.

Question

Answer

3x - 8y = 7

3x - 8y = 25

3x + 8y = 7

3x + 8y = 25

Answer 1

8 y dy + 2 x dx = 0
so
dy/dx = m = -x/4y
at x = 3, y = -2
dy/dx = -3/(4y) = 3/8 = m
so
y = (3/8) x + b
-2 = (3/8)3 + b
b = -25/8
so
y = (3/8) x -25/8
8 y - 3 x = -25
3 x - 8 y = 25 (b)