Find the tangent to the (a) hyberbola x^2-3y^2=4 at(-4,2) (b) Ellipse 9x^2+16y^2=144 at (-3,2)

Answer 1

b) ellipse 9x^2 +16y^2 = 144

16y^2 = 144 - 9x^2

y^2 = 144/16 - 9x^2/16

2yy'= -18x/16

y' = -9x/16y= slope

at (-3,2) the slope = -9(-3)/16(2) = 27/32

tangent line at (-3,2) is

y-2 = (27/32)(x+3) in point slope form

or

y = 27x/32 + 145/32 in slope intercept form

or

27x -32y = -145 in standard form