# How do you find the horizontal and vertical tangents of #4x^2 + y^2 -8x +4y +4=0#?

Horizontal tangents at:

Vertical tangents at:

We have:

Differentiating implicitly:

We can confirm this by completing the square:

graph{4x^2 + y^2 -8x +4y +4=0 [-1, 3, -6, 2]}

By signing up, you agree to our Terms of Service and Privacy Policy

To find the horizontal and vertical tangents of the equation 4x^2 + y^2 -8x +4y +4=0, we can differentiate the equation with respect to x and y separately.

Differentiating with respect to x, we get: 8x - 8 + 0 + 0 = 0 Simplifying, we find: x = 1

Differentiating with respect to y, we get: 0 + 2y + 0 + 4 = 0 Simplifying, we find: y = -2

Therefore, the horizontal tangent occurs at the point (1, -2) and the vertical tangent occurs at the same point (1, -2).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the derivative of the function using the definition of derivative #f(x) = 10#?
- How do you find the equation of the circle with center at (1, 3) and tangent to the line whose equation is x – y + 2 =0?
- Using the limit definition, how do you differentiate #f(x)=x^3−7x+5#?
- How do you find the equations of the tangent to the curve #y = (1 - x)(1 + x^2)-1# that pass through the point (1, 2)?
- How do you use the definition of a derivative to find the derivative of # f(x) = 5x + 9# at x=2?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7