Question

the equatioj of the tangent to tje vurve y2/10 - x2/4 at the point 6,-10

Answer 1

@dumbcow okey so i totualy forgot how to do these

Answer 2

ok equation for tangent line is:
\[y = \frac{dy}{dx}(x - x_1) + y_1\]
(x1,y1) is given point

Answer 3

does the equation = 1 by chance ?
y^2/10 - x^2/4 = 1

Answer 4

ohh sorry yea =1

Answer 5

to get dy/dx you need to take implicit derivative
\[\rightarrow \frac{2y}{10} \frac{dy}{dx} - \frac{2x}{4} = 0\]
solve for dy/dx
\[\frac{dy}{dx} = \frac{(2x/4)}{(2y/10)} = \frac{x}{2}*\frac{5}{y} = \frac{5x}{2y}\]

Answer 6

but doesnt make any difference right

Answer 7

final answer
\[y = (\frac{5x_1}{2y_1})(x - x_1) + y_1\]
plug in given point

Answer 8

what do you mean?

Answer 9

hold on after getting dy/dx what did u do ?

Answer 10

substitute it into equation for tangent line