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in Straight Lines by (92.3k points)
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Line `L` has intercepts `a` and `b` on the coordinate axes. When, the axes area rotated through a given angle, keeping the origin fixed, the same line `L` has intercepts `p` and `q`, then
A. `a^(2)+b^(2)=p^(2)+q^(2)`
B. `(1)/(a^(2))+(1)/(b^(2))=(1)/(p^(2))+(1)/(q^(2))`
C. `a^(2)+p^(2)=b^(2)+q^(2)`
D. `(1)/(a^(2))+(1)/(p^(2))=(1)/(b^(2))+(1)/(q^(2))`

1 Answer

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Best answer
Since the origin remains the same. So, length of the perpendicular from the origin on the line in its position `(x)/(a)+(y)/(b)=1` and `(x)/(p)+(y)/(q)=1` are equal. Therefore,
`(1)/(sqrt((1)/(a^(2))+(1)/(b^(2))))=(1)/(sqrt((1)/(p^(2))+(1)/(q^(2))))implies(1)/(a^(2))+(1)/(b^(2))=(1)/(p^(2))+(1)/(q^(2))`

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