Question

The pair of lines joining the origin to the points of intersection of the curves

ax2 + 2hxy + by2 + 2g x = 0 and a'x2 + 2h'xy + b'y2 + 2g'x = 0 will be at right angles to one another if-

• A. g (a' + b') = g' (a + b)
• B. g (a + b) = g' (a' + b')
• C. gg' = (a + b) (a' + b')
• D. None of these

Answer 1

Answer: (A)

g (a' + b') = g' (a + b)

Answer 2

Homogenize the first curve by the help of second curve,

we get ax2 + 2hxy + by2 + g

$\left[ \frac { - a ^ { \prime } x ^ { 2 } - 2 h ^ { \prime } x y - b ^ { \prime } y ^ { 2 } } { g ^ { \prime } } \right]$ = 0 above equation represents to

two perpendicular lines passing through origin.

Ž coefficient of x2 + coefficient of y2 = 0