SATHEE: Straight Line and Pair of Straight Lines 5 Question 1

Straight Line and Pair of Straight Lines 5 Question 1

1. Let $P Q R$ be a right angled isosceles triangle, right angled at $P (2, 1)$ . If the equation of the line $Q R$ is $2 x + y = 3$ , then the equation representing the pair of lines $P Q$ and $P R$ is

$(1999, 2 M)$

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

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

(d) $3 x^{2} - 3 y^{2} - 8 x y - 10 x - 15 y - 20 = 0$

Show Answer

Answer:

Correct Answer: 1. (b)

Solution:

Let $S$ be the mid-point of $Q R$ and given $△ P Q R$ is an isosceles.

Therefore, $P S ⊥ Q R$ and $S$ is mid-point of hypotenuse, therefore $S$ is equidistant from $P, Q, R$ .

$\begin{array}{lc} ∴ & P S = Q S = R S \\ Since, & ∠ P = 90^{\circ} and ∠ Q = ∠ R \\ But & ∠ P + ∠ Q + ∠ R = 180^{\circ} \end{array}$

Now, slope of $Q R$ is -2 .

[given]

But $Q R ⊥ P S$ .

$∴$ Slope of $P S$ is $1 / 2$ .

Let $m$ be the slope of $P Q$ .

$∴ \tan (\pm 45^{\circ}) = \frac{m - 1 / 2}{1 - m (- 1 / 2)}$

$\Rightarrow \pm 1 = \frac{2 m - 1}{2 + m}$

$\Rightarrow m = 3, - 1 / 3$

$∴$ Equations of $P Q$ and $P R$ are

$\begin{aligned} y - 1 = 3 (x - 2) \\ and y - 1 = - \frac{1}{3} (x - 2) \\ or 3 (y - 1) + (x - 2) = 0 \end{aligned}$

Therefore, joint equation of $P Q$ and $P R$ is

$[3 (x - 2) - (y - 1)] [(x - 2) + 3 (y - 1)] = 0$

$\Rightarrow 3 (x - 2)^{2} - 3 (y - 1)^{2} + 8 (x - 2) (y - 1) = 0$

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

Download Chapter Test

http://tinyurl.com/y5bdtgdz

16

पिछला

अगला

Straight Line and Pair of Straight Lines 5 Question 1

1. Let $P Q R$ be a right angled isosceles triangle, right angled at $P (2, 1)$ . If the equation of the line $Q R$ is $2 x + y = 3$ , then the equation representing the pair of lines $P Q$ and $P R$ is

Answer:

16

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Straight Line and Pair of Straight Lines 5 Question 1

1. 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

Answer:

16

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

1. Let $P Q R$ be a right angled isosceles triangle, right angled at $P (2, 1)$ . If the equation of the line $Q R$ is $2 x + y = 3$ , then the equation representing the pair of lines $P Q$ and $P R$ is