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Question
The length of the perpendicular from the origin on the line `(xsinalpha)/"b" - (ycosalpha)/"a" - 1 = 0` is ______.
Options
`|"ab"|/sqrt("a"^2 cos^2 alpha - "b"^2 sin^2alpha)`
`|"ab"|/sqrt("a"^2 cos^2 alpha + "b"^2 sin^2alpha)`
`|"ab"|/sqrt("a"^2 sin^2 alpha - "b"^2 cos^2alpha)`
`|"ab"|/sqrt("a"^2 sin^2 alpha + "b"^2 cos^2alpha)`
MCQ
Fill in the Blanks
Solution
The length of the perpendicular from the origin on the line `(xsinalpha)/"b" - (ycosalpha)/"a" - 1 = 0` is `|"ab"|/sqrt("a"^2 sin^2 alpha + "b"^2 cos^2alpha)`.
Explanation:
Given, equation of line is
`(xsinalpha)/"b" - (ycosalpha)/"a" - 1 = 0`
∴ perpendicular distance from origin
= `|(0* sinalpha/"b" - (0*cosalpha)/"a" - 1)/sqrt((sin^2alpha)/"b"^2 + (cos^2alpha)/"a"^2)|`
= `|"ab"|/sqrt("a"^2sin^2alpha + "b"^2 cos^2alpha)`
shaalaa.com
General Form of Equation of a Line
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