All the answers to your questions. The ones you did are correct as well
X² + 8x +y² - 2y -64 =0
We see that the equation has x² and y² . Also we see that coefficients in front of x² and y² are equal. So this is an equation of the circle.
(x² + 8x) +(y² - 2y) -64 =0
(x² + 8x) +(y² - 2y) = 64
We need to complete square for x and y groups, that means it should be written in form (a+b)² or (a-b)².
Expressions in parenthesis we will write as a²+/-2ab+b², to write it after as (a+/-b)², because a²+/-2ab+b² = (a+/-b)²
(x² + 2*4x) +(y² - 2*1y) = 64
(x² + 2*4x+4²) +(y² - 2*1y+1²) = 64+4²+1²
(x+4)² + (y-1)²= 81 Sometimes this is called a standard form of the circle.
(x+4)² + (y-1)²= 9² Sometimes it is required to write like this.
And if you are studying circles,ellipses and hyperbolas, the standard form should look like
Answer:
(25x2 + 4y2) (5x + 2y) (−5x + 2y)
Step-by-step explanation:
Factor 16y4−625x4
−625x4 + 16y4
=(25x2 + 4y2) (5x + 2y) (−5x + 2y)
The equation of the line that is perpendicular to 4x - 3y = 10 through the point (-2,4) is 
<u>Solution:</u>
Given, line equation is 4x – 3y = 10
We have to find a line that is perpendicular to 4x – 3y = 10 and passing through (-2, 4)
Now, let us find the slope of the given line,

We know that, slope of a line
slope of perpendicular line = -1

Now, slope of our required line =
and it passes through (-2, 4)
<em><u>The point slope form is given as:</u></em>


Hence the equation of line is found out