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Intercept Made by Circle on Axes

If the line ...

Question

If the line $x - 2 y = k$ cuts off a chord of length $2$ units from the circle $x^{2} + y^{2} = 3$ , then $k =$

0

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\pm 1

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\sqrt{10}

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None of these

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Solution

The correct option is C $\sqrt{10}$

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Similar questions

If the line $x - 2 y = k$ cuts off a chord of length 2 from the circle $x^{2} + y^{2} = 3$ , then k =

x^{2} + y^{2} = a^{2}

2 b

y = m x + c

x^{2} + y^{2} + 4 x - 2 y - 3 = 0

y = x + 2

x + 2 k y + 3 = 0

x^{2} + y^{2} - 6 x + 2 y = 0

k

x + y = 0

(\frac{1 + k \sqrt{2}}{2}, \frac{1 - k \sqrt{2}}{2})

x^{2} + y^{2} - (\frac{1 + k \sqrt{2}}{2}) x - (\frac{(1 - k \sqrt{2})}{2}) y = 0.

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