Equation of circle :
Equation of circle which is having center as (0, 0) and radius r will be in the form.
x2 + y2 = r2
Equation of circle which is having center as (h, k) and radius r will be in the form.
Classify each conic section and write its equation in standard form.
Problem 1 :
25x2 + 9y2 - 36y - 189 = 0
Solution:
25x2 + 9y2 - 36y - 189 = 0
25x2 + 9y2 - 36y = 189
25x2 + 9(y2 - 4y) = 189
25x2 + 9(y2 - 2 • y • 2 + 22 - 22) = 189
25x2 + 9[(y - 2)2 - 4] = 189
By distributing 9, we get
25x2 + 9(y - 2)2 - 36 = 189
25x2 + 9(y - 2)2 = 189 + 36
25x2 + 9(y - 2)2 = 225
Hence, it is Ellipse.
Problem 2 :
-2x2 + 20x + y - 44 = 0
Solution:
-2x2 + 20x + y - 44 = 0
It is parabola. It is symmetric about y-axis.
Problem 3 :
-y2 + 2x + 2y + 3 = 0
Solution:
-y2 + 2x + 2y + 3 = 0
It is parabola. It is symmetric about x-axis.
Problem 4 :
16x2 + 9y2 - 16x + 18y - 131 = 0
Solution:
16x2 + 9y2 - 16x + 18y - 131 = 0
16x2 - 16x + 9y2 + 18y = 131
Now add (1/2)2 and 12 to each side to complete the square on the left side of the equation.
It is Ellipse. Here a2 = 9 and b2 = 16. Since b2 is greater than a2, the ellipse is symmetric about y-axis.
Problem 5 :
x2 + y2 - 8x + 8y + 31 = 0
Solution:
x2 + y2 - 8x + 8y + 31 = 0
It is equation of circle with center (4, -4).
Problem 6 :
2x2 + 2y2 - 14x - 2y + 7 = 0
Solution:
2x2 + 2y2 - 14x - 2y + 7 = 0
It is circle with the center (7/2, 1/2) and radius 3.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM