Question

The point of intersection of lines given by the equation 2x² + 4xy - 2y² + 4x + 8y + 1 = 0 is ______

विकल्प

• `(3/2, 1/2)`

• `((-3)/2, 1/2)`

• `(3/4, 1/4)`

• `(3/4, (-1)/4)`

Answer 1

The point of intersection of lines given by the equation 2x² + 4xy - 2y² + 4x + 8y + 1 = 0 is `underline(((-3)/2, 1/2))`.

Explanation: 

Comparing the given equation with

ax² + 2hxy + by² + 2gx + 2fy + c = 0, we get

a = 2, h = 2, b = -2, g = 2, f = 4, c = 1

Point of intersection of lines is given by

`((hf - bg)/(ab - h^2), (gh - af)/(ab - h^2))`

= `((8 + 4)/(-4 - 4), (4 - 8)/(-4 - 4))`

= `((-3)/2, 1/2)`