Question

The point of intersection of line represented by x² – y² + 3y – 2 = 0 is ______.

Options

• (1, 0)

• (0, 2)

• `(-1/2, 3/2)`

• `(1/2, 1/2)`

Answer 1

The point of intersection of line represented by x² – y² + 3y – 2 = 0 is `underlinebb((-1/2, 3/2)`.

Explanation:

x² – y² + x + 3y – 2 = 0

Comparing the above equation with

ax² + 2hxy + by² + 2gx + 2fy + c = 0

we get

a = 1, h = 0, b = –1, g = `1/2`, f = `3/2`, c = –2

∴ Required point of intersection is:

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

`≡ ((0 + 1/2)/(-1), (0 - 3/2)/(-1)) ≡ (-1/2, 3/2)`