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ludmilkaskok [199]
3 years ago
15

HELP Which equations represent hyperbolas?

Mathematics
2 answers:
MissTica3 years ago
7 0
An elliptical equation is in the form
Ax^2+Bx+Cy^2+Dy+E=0
the equation is a Hyperbola. When x and y are both squared, and exactly one of the coefficients is negative and exactly one of the coefficients is positive.
1-49x^2-98x-64y^2+256y-2831=0
2-4x^2+32x-25y^2-250y+589=0
3-81x^2+512x-64y^2-324y-3836=0
Hoochie [10]3 years ago
5 0

Answer: The required equations of hyperbolas would be

49x^2-98x-64y^2+256y-2831=0\\\\4x^2+32x-25y^2-250y+589=0\\\\81x^2+512x-64y^2-324y-3836=0

Step-by-step explanation:

Since we know that

The general equation for a conic section:

Ax^2+Bxy+Cy^2+Dx+Ey+F=0

In case of hyperbola, we get that

Discriminant=B^2-4AC>0

According to this, both x and y are squared.

And one of the coefficient of x and y must be positive and one of the coefficient of x and y must be negative.

So, the required equations of hyperbolas would be

49x^2-98x-64y^2+256y-2831=0\\\\4x^2+32x-25y^2-250y+589=0\\\\81x^2+512x-64y^2-324y-3836=0

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What is the translation of the point to its image? A (−1, 4)→ A' (3, 3)
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Answer:

We validate that the formula to determine the translation of the point to its image will be:

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Step-by-step explanation:

Given

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Here:

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  • A'(3, 3) is the image of A

We need to determine which translation operation brings the coordinates of the image A'(3, 3).

If we closely observe the coordinates of the image A' (3, 3), it is clear the image coordinates can be determined by adding 4 units to the x-coordinate and subtracting 1 unit to the y-coordinate.

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A(x, y) → A' (x+4, y-1)

Let us check whether this translation rule validates the image coordinates.

A (x, y) → A' (x+4, y-1)

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