Question

The equation to the circle which belongs to the coaxal system of which the limiting points are (1, –1), (2, 0) and which passes through the origin is –

• A. x² + y² –4x = 0
• B. x² + y² + 4x = 0
• C. x² + y² –4y = 0
• D. x² + y² + 4y = 0

Answer 1

Answer: (D)

x² + y² + 4y = 0

Answer 2

The point circles represented by the limiting points are

(x –1)² + (y + 1)² = 0 and

(x –2)² + y² = 0. So the equation of coaxal system is,

(x –1)² + (y + 1)² + l {(x –2)² + y²} = 0 …(1)

It passes through (0, 0), so, l = –$\frac{1}{2}$ putting into (1),

we get the equation to the desired circle as x² + y² + 4y = 0