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Standard XII

Mathematics

Length of Intercept Made by a Circle on a Straight Line

Let L1 be a s...

Question

Let $L_{1}$ be a straight line passing through the origin and $L_{2}$ be the straight line x + y = 1. If the intercepts made by

the circle $x^{2} + y^{2} - x + 3 y = 0$ on $L_{1}$ and $L_{2}$ are equal, then which of the following equations can represent $L_{1}$

x + y = 0

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x - y = 0

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x + 7y = 0

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x - 7y = 0

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Solution

The correct option is B
x - y = 0

$x + y = 1, x^{2} + y^{2} - x + 3 y = 0 x^{2} + (1 - x)^{2} - x + 3 (1 - x) = 0 x^{2} + 1 + x^{2} - 2 x - x + 3 - 3 x = 0 2 x^{2} - 6 x + 4 = 0 x^{2} - 3 x + 2 = 0 x = 1, 2 A (1, 0), B (2, - 1) A B = \sqrt{1 + 1} = \sqrt{2} ∴ y = x 2 x^{2} + 2 x = 0 x = 0, - 1 y = x (0, 0), (- 1, - 1) \sqrt{1 + 1} = \sqrt{2}$

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Similar questions

Let $L_{1}$ be a straight line passing through the origin and $L_{2}$ be the straight line x + y = 1. If the intercepts made by

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Let L1 be a straight line passing through the origin and L2 be the straight line x + y = 1. If the intercepts made by the circle x2+y2−x+3y=0 on L1 and L2 are equal, then which of the following equations can represent L1

The correct option is B x - y = 0 x+y=1, x2+y2−x+3y=0x2+(1−x)2−x+3(1−x)=0x2+1+x2−2x−x+3−3x=02x2−6x+4=0x2−3x+2=0x=1,2A(1,0),B(2,−1)AB=√1+1=√2∴y=x2x2+2x=0x=0,−1y=x(0,0),(−1,−1)√1+1=√2

Let $L_{1}$ be a straight line passing through the origin and $L_{2}$ be the straight line x + y = 1. If the intercepts made by

the circle $x^{2} + y^{2} - x + 3 y = 0$ on $L_{1}$ and $L_{2}$ are equal, then which of the following equations can represent $L_{1}$