SATHEE: Straight Line and Pair of Straight Lines 4 Question 1

Straight Line and Pair of Straight Lines 4 Question 1

1. Let $a$ and $b$ be non-zero and real numbers. Then, the equation $(a x^{2} + b y^{2} + c) (x^{2} - 5 x y + 6 y^{2}) = 0$ represents

(2008, 3M)

(a) four straight lines, when $c = 0$ and $a, b$ are of the same sign

(b) two straight lines and a circle, when $a = b$ and $c$ is of sign opposite to that of $a$

(d) a circle and an ellipse, when $a$ and $b$ are of the same sign and $c$ is of sign opposite to that of $a$

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Answer:

Correct Answer: 1. (b)

Solution:

Let $a$ and $b$ be non-zero real numbers.

Therefore the given equation

$\begin{aligned} (a x^{2} + b y^{2} + c) (x^{2} - 5 x y + 6 y^{2}) = 0 implies either \\ x^{2} - 5 x y + 6 y^{2} = 0 \\ \Rightarrow (x - 2 y) (x - 3 y) = 0 \\ \Rightarrow x = 2 y \\ and x = 3 y \end{aligned}$

represent two straight lines passing through origin or $a x^{2} + b y^{2} + c = 0$ when $c = 0$ and $a$ and $b$ are of same signs, then

$\begin{aligned} a x^{2} + b y^{2} + c & = 0 \\ x & = 0 \end{aligned}$

$and y = 0 .$

which is a point specified as the origin.

When, $a = b$ and $c$ is of sign opposite to that of $a$ , $a x^{2} + b y^{2} + c = 0$ represents a circle.

Hence, the given equation,

$(a x^{2} + b y^{2} + c) (x^{2} - 5 x y + 6 y^{2}) = 0$

may represent two straight lines and a circle.

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Straight Line and Pair of Straight Lines 4 Question 1

1. Let $a$ and $b$ be non-zero and real numbers. Then, the equation $(a x^{2} + b y^{2} + c) (x^{2} - 5 x y + 6 y^{2}) = 0$ represents

Answer:

इंजीनियरिंग की तैयारी

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एनसीईआरटी पुस्तकें और समाधान

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अन्य संसाधन

पाठ्यक्रम

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नमूना मॉक टेस्ट

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एनसीईआरटी व्यायाम वीडियो समाधान

Straight Line and Pair of Straight Lines 4 Question 1

1. Let a and b be non-zero and real numbers. Then, the equation (ax2+by2+c)(x2−5xy+6y2)=0 represents

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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1. Let $a$ and $b$ be non-zero and real numbers. Then, the equation $(a x^{2} + b y^{2} + c) (x^{2} - 5 x y + 6 y^{2}) = 0$ represents