Question

If there are two points A and B on rectangular hyperbola

xy = c² such that abscissa of A = ordinate of B, then locus of point of intersection of tangents at A & B is –

• A. y² –x² = 2c²
• B. y² –x² = $\frac{c^{2}}{2}$
• C. y = x
• D. None of these

Answer 1

Answer: (C)

y = x

Answer 2

Let A is (a, b) then B is (b, a)

\A & B are symmetric about y = x,

so tangents at A and B will be mirror images of each other, about y = x. Thus point of intersection will lie on y = x.