Write the equation for a parabola with a vertex of (-5,-4) and a focus of (-5,-2)

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

4 0

The equation of the parabola is (x + 5)² = 8(y + 4)

Step-by-step explanation:

Let us revise the equation of the parabola in standard form

The standard form is (x - h)² = 4p(y - k)
The vertex is (h , k)
The focus is (h, k + p)

∵ The vertex of the parabola is (-5 , -4)

- The coordinates of the vertex are (h , k)

∴ h = -5 and k = -4

∵ The focus is (-5 , -2)

- The focus is (h , k + p)

∴ k + p = -2

∵ k = -4

∴ -4 + p = -2

- Add 4 to both sides

∴ p = 2

- Substitute the values of h , k , p in the form of the equation

∵ The equation of the parabola is (x - h)² = 4p(y - k)

∴ (x - -5)² = 4(2)(y - -4)

∴ (x + 5)² = 8(y + 4)

The equation of the parabola is (x + 5)² = 8(y + 4)

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IgorLugansk [536]

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Step-by-step explanation:

As per the problem, the given triangle is a right triangle. This is signified by the box around one of its angles, this box states that the angle it is surrounding is a right angle.

Since it is a right triangle, one can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that; ( $a^2 + b^2 = c^2$ ), where ( $a$ ) and ( $b$ ) are the legs of the right triangle, or the sides adjacent to the right angle. ( $c$ ) is the hypotenuse or the side opposite the right angle.