Question

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

Answer 1

Greetings!

Answer:

The standard form equation is B.

The centre of the circle is B

The radius is B.

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
`(1)/(2)* b`

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
`a` and
`b`

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^{(1)/(2) } )`

So your answer is B.

Hope this helps!