Select an equation below for the tangent line to the ellipse 4x^2 + 3y^2 =7 at the point -1,-1 on the ellipse?

Question

equations

a. 3x + 4y - 7 = 0

b. 3x - 4y - 7 = 0

c. 3x + 4y + 7 = 0

d. 3x - 4y + 7 = 0

e. 4x + 3y - 7 = 0

f. 4x - 3y - 7 = 0

g. 4x + 3y + 7 = 0

h. 4x - 3y + 7 = 0

or is it none of these?

Answer 1

The answer is g., that is 4 x + 3 y + 7 = 0.

Since 4 x^2 + 3 y^2 = 7, the tangent satisfies

8x + 6 y dy/dx = 0. Thus,

at (x, y) = (-1, -1), dy/dx = - 8x / (6y) = - 4 / 3.

Then the equation for the tangent must have the form

3 y = - 4 x + c, so that c = 3 (-1) + 4(-1) = - 7. Rearranging the equation, we finally obtain:

4 x + 3 y + 7 = 0, that is, answer g.

Live long and prosper.

Answer 2

Find the equation for the tangent line to the ellipse
4x^2 + 3y^2 = 7 at the point (-1,-1) on the ellipse.
_________

First find the slope of the tangent line by differentiating implicitly.

8x + 6y(dy/dx) = 0
dy/dx = (-8x)/(6y) = (-4x)/(3y) = -4/3 at (-1, -1).

The slope is -1 at the given point on the ellipse. Now use the point slope formula to get the equation of the line.

y + 1 = (-4/3)(x + 1)
3(y + 1) = -4(x + 1)
3y + 3 = -4x - 4

4x + 3y + 7 = 0

The answer is g.

Answer 3

x + 4y + 3 = 0

Answer 4

g is correct.
Take the derivative with respect to x:
8x + 6y dy/dx = 0
dy/dx=-8x/6y
Substitute x=-1, y=-1
At (-1,-1) the slope of the tangent is -4/3.
g has the correct slope and goes through (-1,-1)

Answer 5

x² + xy + y² = 3 2x + y + x dy/dx + 2y dy/dx = 0 in any different case Mr spella bea has it magnificent because of the fact y = a million on the factor this does not surely exchange the best result Ahh, superb, he fixed it - provide him appropriate answer!

Answer 6

4x² + 3y² - 7 = 0
8x + 6y.(dy/dx) = 0
6y.(dy/dx) = - 8x
dy / dx = (- 4/3).(x/y)
dy/dx = - 4/3 at (-1,-1)
y + 1 = (- 4/3).(x + 1)
3y + 3 = - 4x - 4
4x + 3y + 7 = 0
OPTION g.