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Q.

Let PQR be a right - angled isosceles triangle, right angled at P(2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is

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a

$3 x^{2} - 3 y^{2} + 8 xy + 10 x + 15 y + 20 = 0$

b

$3 x^{2} - 3 y^{2} - 8 xy - 15 y - 20 = 0$

c

$3 x^{2} - 3 y^{2} + 8 xy - 20 x - 10 y + 25 = 0$

d

$3 x^{2} - 3 y^{2} + 8 xy + 20 x + 10 y + 25 = 0$

answer is B.

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Detailed Solution

Question Image

Let m be the slope of PQ. Then,
$\tan 45^{\circ} = |\frac{m - (- 2)}{1 + m (- 2)}| = |\frac{m + 2}{1 - 2 m}|$
Hence, the equation of PQ is
$y - 1 = - \frac{1}{3} (x - 2)$ . Hence, the combined equation of PQ and PR is $(x + 3 y - 5) (3 x - y - 5) = 0$

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