SATHEE: Straight Line and Pair of Straight Lines 4 Question 2

Straight Line and Pair of Straight Lines 4 Question 2

2. Area of triangle formed by the lines $x + y = 3$ and angle bisectors of the pair of straight lines $x^{2} - y^{2} + 2 y = 1$ is

(a) 2 sq units

(b) 4 sq units

(d) 8 sq units

(2004, 2M)

Analytical & Descriptive Question

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Answer:

Correct Answer: 2. (a)

Solution:

Given, $x^{2} - y^{2} + 2 y = 1$

$\begin{aligned} \Rightarrow & x^{2} & = (y - 1)^{2} \\ \Rightarrow & x & = y - 1 and x = - y + 1 \end{aligned}$

Angle bisector

From the graph, it is clear that equation of angle bisectors are

$\begin{array}{ll} y = 1 \\ and & x = 0 \end{array}$

$∴$ Area of region bounded by $x + y = 3, x = 0$ and $y = 1$ is $Δ = \frac{1}{2} \times 2 \times 2 = 2$ sq units

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Straight Line and Pair of Straight Lines 4 Question 2

2. Area of triangle formed by the lines $x + y = 3$ and angle bisectors of the pair of straight lines $x^{2} - y^{2} + 2 y = 1$ is

Analytical & Descriptive Question

Answer:

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 4 Question 2

2. Area of triangle formed by the lines x+y=3 and angle bisectors of the pair of straight lines x2−y2+2y=1 is

Analytical & Descriptive Question

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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2. Area of triangle formed by the lines $x + y = 3$ and angle bisectors of the pair of straight lines $x^{2} - y^{2} + 2 y = 1$ is