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Convert the equation into standard form.
25x^2 - 9y^2 + 200x + 18y + 166 = 0

Sagot :

clarussa1221

Answer:

the answer is d (x+4)^2/9 - (y-1)^2/25

Step-by-step explanation:

its correct on edge

shubhamchouhanvrVT

The standard form of the given equation is [tex]\dfrac{(x+4)^2}{9}-\dfrac{(y+1)^2}{25}=1[/tex]

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Begin by grouping the x terms together and the y terms together, and getting the constant on the other side of the equals sign:

25x² +200x - 9y² +18y = -166

Now we need to complete the square on the x terms and the y terms. Do this by first factoring out the leading coefficient from each, the 25 from the x's and the 9 from the y's:

25(x² +8x) - 9 (y² +2y) = -166

Now take half the linear term in each set of parenthesis, square it, and add it to both sides, remembering the multiplier outside (the 25 and the 9). Our x linear term is 8. Half of 8 is 4, and 4 squared is 16, so we add a 16 into the parenthesis with the x's; our y linear term is 2. Half of 2 is 1 and 1 squared is 1, so we add a 1 into the parenthesis with the y's:

25(x² +8x + 16)-9(y²+2y +1) = -166+400-9

Note the 400 and -9 on the right side now. 25 times 16 is 400; we didn't just add in a 16, we have to multiply the scalar number into it before we know what we really added in. And the -9 comes from multiplying the -9 times 1.

The reason we do this is to get the perfect square binomials on the left that we created while completing the square:

25(x+4)² - 9 (y+1)²= 225

Now, finally, we will divide both sides by 225 to get this conic into the standard form:

[tex]\dfrac{(x+4)^2}{9}-\dfrac{(y+1)^2}{25}=1[/tex]

This is a hyperbola with a horizontal transverse axis and a center of (-4, -1). The reason we know it's not an ellipse is because an ellipse will always have a + sign separating the x-squared from the y-squared whereas a hyperbola always has a - sign separating them. And we also know it's not a circle because the values of the leading coefficients weren't the same.

Therefore the standard form of the given equation is[tex]\dfrac{(x+4)^2}{9}-\dfrac{(y+1)^2}{25}=1[/tex]

To know more about Expression follow

https://brainly.com/question/723406

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