Question

UVU
6. For parabola x2 + y2 + 2xy - 6x - 2y + 3 = 0, the focus is
(a) (1 - 1)
(b)(-1,1)
(c)(3,1)​

Answer 1

Step-by-step explanation:

Given For parabola x2 + y2 + 2xy - 6x - 2y + 3 = 0, the focus is

• Now if we draw a parabola we have ps = pm
• Also equation will be y = mx + c
• Now focus will be f(h,k)
• Now we have the equation
•     So √(x – h)^2 + (y – k)^2 =  y – mx – c / √1 + m^2 (distance ps = pm)
• So we get
•      So x^2 + m^2y^2 + 2mxy – 2 xh(1 + m^2) + mc – 2y(k(1 + m^2) – c) + 9x^2 + k^2) (1 + m^2 – c^2) = 0
• Comparing the coefficients from the given equation of parabola we get
•    So m^2 = 1
•    Or m = +-1
• Now coefficient of xy is 2
•    So 2m = 2
•    Or m = 1
• Coefficient of x = - 6
• So 2h (1 + m^2) + 2c = 6
•   Or 2h + c = 3 -----------------1
• Comparing the coefficient of y we get
•      2k (1 + m^2) – 2c  
•      2k – c = 1--------------------2
•      2(h^2 + k^2) – c^2 -----------3
• So 2 [ (3 – c / 2)^2 + (1 + c / 2)^2 – c^2 = 3
•  So ½ [9 + c^2 – 6c + 1 + c^2 + 2c) – c^2 = 3
•  So c^2 – 2c + 5 – c^2 = 3
• Or 2c = 2
•  Or c = 1
• So 2h = 2
•     Or h = 1
• Also 2k = 2
•      So k = 1
• So focus of parabola will be f(1,1) or (1,1)

Reference link will be

https://brainly.in/question/7390452

Answer 2

Answer:

-1,1 will be the correct answer