First slide

Pair of straight lines

Question

The equation ${ax}^{2} + 2 hxy + {by}^{2} + 2 gx + 2 fy + c = 0$ represents a pair of parallel lines then $\sqrt{ab} =$

Easy

A

h
B

$\frac{h}{2}$
C

$h^{2}$
D

2h

Solution

The condition that the equation ${ax}^{2} + 2 hxy + {by}^{2} + 2 gx + 2 fy + c = 0$ represents pair of $h^{2} = ab, and {af}^{2} = {bg}^{2}$ parallel lines is
Hence, $h = \sqrt{ab}$
Therefore $\sqrt{ab} = h$

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