Question Of The Day

Points (a, b) and (p, q) satisfy the two equations y = x² and x = y². What is the equation of the line passing through (a, b) and (p, q)?  

a) y = x

b)  y + x = 0

c) y = 2x

d) y = 3x + 5

Ans: a) y = x

From y = x² and y² = x, we get y (y²)²; i.e. y(y³ – 1) = 0; ∴ y = 0 or y = + 1.

Substituting, we get x = 0 or x = +1.

the points are (a, b) = (0, 0); (p, q) = (1, 1) and the line through them is y = x.