NIMCET 2007 — Mathematics PYQ

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Question

NIMCET 2007 — Mathematics PYQ

NIMCET | Mathematics | 2007

The distance between the pair of straight lines $x^{2} + 23 x y + 2 y^{2} + 4 x + 1 = 0$ is:

Choose the correct answer:

Explanation

Given equation:

$x^{2} + 23 x y + 2 y^{2} + 4 x + 1 = 0$

Comparing with $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ :

$a = 1$
$h = 3$
$b = 2$
$g = 2$
$f = 0$
$c = 1$

Check condition for parallel lines:

$h^{2} = (3)^{2} = 3$

$ab = 1 \times 2 = 2$

Since $h^{2} \neq = ab$ , the lines are not parallel.

Check for standard typo ( $b = 3$ instead of $2$ ):

If the equation is $x^{2} + 23 x y + 3 y^{2} + 4 x + 1 = 0$ :

$a = 1, b = 3, g = 2, c = 1$

Formula for distance between parallel lines:

$d = 2 \frac{g ^{2} - a c}{a ( a + b )}$

$d = 2 \frac{2 ^{2} - 1 ( 1 )}{1 ( 1 + 3 )}$

$d = 2 \frac{4 - 1}{4} = 2 \times \frac{3}{2} = 3$

Correct Answer:

(d) none (or (c) $3$

Choose the correct answer:

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