Equation of circle :
Equation of circle which is having center as (0, 0) and radius r will be in the form.
x^{2} + y^{2} = r^{2}
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 :
25x^{2} + 9y^{2} - 36y - 189 = 0
Solution:
25x^{2} + 9y^{2} - 36y - 189 = 0
25x^{2} + 9y^{2} - 36y = 189
25x^{2} + 9(y^{2} - 4y) = 189
25x^{2} + 9(y^{2} - 2 • y • 2 + 2^{2} - 2^{2}) = 189
25x^{2} + 9[(y - 2)^{2} - 4] = 189
By distributing 9, we get
25x^{2} + 9(y - 2)^{2} - 36 = 189
25x^{2} + 9(y - 2)^{2} = 189 + 36
25x^{2} + 9(y - 2)^{2} = 225
Hence, it is Ellipse.
Problem 2 :
-2x^{2} + 20x + y - 44 = 0
Solution:
-2x^{2} + 20x + y - 44 = 0
It is parabola. It is symmetric about y-axis.
Problem 3 :
-y^{2} + 2x + 2y + 3 = 0
Solution:
-y^{2} + 2x + 2y + 3 = 0
It is parabola. It is symmetric about x-axis.
Problem 4 :
16x^{2} + 9y^{2} - 16x + 18y - 131 = 0
Solution:
16x^{2} + 9y^{2} - 16x + 18y - 131 = 0
16x^{2} - 16x + 9y^{2} + 18y = 131
Now add (1/2)^{2} and 1^{2} to each side to complete the square on the left side of the equation.
It is Ellipse. Here a^{2} = 9 and b^{2} = 16. Since b^{2} is greater than a^{2}, the ellipse is symmetric about y-axis.
Problem 5 :
x^{2} + y^{2} - 8x + 8y + 31 = 0
Solution:
x^{2} + y^{2} - 8x + 8y + 31 = 0
It is equation of circle with center (4, -4).
Problem 6 :
2x^{2} + 2y^{2} - 14x - 2y + 7 = 0
Solution:
2x^{2} + 2y^{2} - 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