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Jadaflournoy5
14.07.2019 •
Mathematics
The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0 the equation of this circle in standard form is a. (x - 2)^2 + (y + 3)^2 = 5 b. (x - 2)^2 + (y + 3)^2 = 18 c. (x - 4)^2 + (y + 6)^2 = 24 d. (x + 4)^2 + (y - 6)^2 = 24 e. (x + 2)^2 + (y - 3)^2 = 35 the center of the circle is at the point __ a. (-14,21) b. (-2,3) c. (2,-3) d. (-4,6) e. (4,-6) and it's radius is units. a. 5 1/2 b. 3(2 1/2) c. 2(6 1/2) d. 35 1/2
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Ответ:
The standard form equation is B.
The centre of the circle is B
The radius is B.
Step-by-step explanation:
Firstly, the equation can all be divided by 7:
(7x² + 7y²− 28x + 42y − 35) ÷ 7 =
x² + y² - 4x + 6y - 5 = 0
x² - 4x + y² + 6y - 5 = 0
Now add![\frac{1}{2}* b](/tpl/images/0089/0920/e34e1.png)
0.5 * 4 = 2, 2² = 4 so 4
0.5 * 6 = 3. 3² = 9 so 9
(x² - 4x + 4) + (y² + 6y + 9) - 4 - 9 - 5 = 0
As the standard form of a circle is (x - a)² + (y - b)²= r² , we need to change this to this. Simply find a number that multiplies to 4 and adds to -4 ( -2 ) and a number that multitplies to 9 and adds to 6 (3):
(x - 2)² + (y + 3)²
Also, we need to subtract the square of the number inside the brackets, as this is completing the square:
-2 * -2 = 4
3 * 3 = 9
So we need to subtract 4 and 9, and 5 as that was in the original:
(x - 2)² + (y + 3)² - 4 - 9 - 5 = 0
To find the radius, we need to move this numbers over to the other side making them positives:
(x - 2)² + (y + 3)² = 4 + 9 + 5
(x - 2)² + (y + 3)² = 18
So the equation is B.The centre of the circle in (x - a)² + (y - b)² is
and ![b](/tpl/images/0089/0920/d3a66.png)
So in this equation the centre is -2, 3. Which is B.The radius is the square root of whatever (x - a)² + (y - b)² equals, so the square root of 18 is the radius:
√18 = √9√2
= 3√2
=![3 * (2x^{\frac{1}{2} } )](/tpl/images/0089/0920/aa8b6.png)
So your answer is B.Hope this helps!
Ответ:
Answers: a
Step by step explanation,.