Question

The line L has intercepts a and b on the co-ordinate axes. Keeping the origin fixed, the co-ordinate axes are rotated through a fixed angle. The line L has now intercepts p and q on the rotated axes. Then

• A. a² + b² = p² + q²
• B. 1/a² + 1/b² = 1/p² +1/q²
• C. a² +p² = b² + q²
• D. 1/a² + 1/p² = 1/b² + 1/q²

Answer 1

Answer: (B)

1/a² + 1/b² = 1/p² +1/q²

Answer 2

The equation of the line L is x/a + y/b = 1. . . . . . (1)

After the rotation of the axes, the line L has intercepts p and q on the new axes.

In this system equation of the line is x/p + y/q = 1.

Since the origin and the line, both are fixed, the distance between them remains the same.

⇒ $\left| \frac { - 1 } { \sqrt { \frac { 1 } { \mathrm { a } ^ { 2 } } + \frac { 1 } { \mathrm {~b} ^ { 2 } } } } \right| = \left| \frac { - 1 } { \sqrt { \frac { 1 } { \mathrm { p } ^ { 2 } } + \frac { 1 } { \mathrm { q } ^ { 2 } } } } \right|$ ⇒