Q89 / 160 · TS EAMCET 2022 (18 Jul Shift 1) · Mathematics

The equation $x^{2} - y^{2} + a x + b = 0$ represents a pair of lines for the ordered pair $(a, b) =$

A
$(2, 6)$
B
$(3, 4)$
C
$(4, 8)$
Correct answer
D
$(6, 9)$

Solution

Given,
$x^{2} - y^{2} + a x + b = 0$ represents pair of straight line
We know that if $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ represent a pair of straight line then $△ = 2 f g h + a b c - a f^{2} - b g^{2} - c h^{2} = 0$
So, on comparing with given equation we get,
$△ = 0 + 1 \times (- 1) \times b - 0 + 1 {(\frac{a}{2})}^{2} = 0$
$\Rightarrow a^{2} - 4 b = 0$
So, only $(6, 9)$ will satisfy the given equation.

Hence, the correct answer is option: 'D'.

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The equation x2-y2+ax+b=0 represents a pair of lines for the ordered pair a,b=

Solution

Relevant Questions

The equation $x^{2} - y^{2} + a x + b = 0$ represents a pair of lines for the ordered pair $(a, b) =$