First slide

Pair of straight lines

Question

If a, h, b are in A.P. then the triangle area formed by the pair of lines $a x^{2} + 2 h x + b y^{2} = 0$ and the line $x - y = - 2$ in square units is

Moderate

A

$|\frac{a + b}{a - b}|$
B

$|\frac{a^{2} + b^{2}}{a - b}|$
C

$|\frac{a - b}{a + b}|$
D

$|\frac{a^{2} + b^{2}}{a + b}|$

Solution

a, h, b are in A.P
$2 h = a + b$ , $l = 1, m = - 1, n = 2$
$\frac{n^{2} \sqrt{h^{2} - a b}}{|a m^{2} - 2 h l m + b l^{2}|}$

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