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Question
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
Options
a2 + b2
a + b
a2 − b2
- \[\sqrt{a2 + b2}\]
Solution
We have to find the distance betweenA` (a cos theta + b sin theta , 0 ) " and " B(0, a sin theta - b cos theta )` .
In general, the distance between A(x1 , y 1) and B(x2 , y2) is given by,
`AB = sqrt((x_2 - x_1 )^2 + (y_2 - y_1 )^2)`
So,
`AB = sqrt((a cos theta + b sin theta - 0)^2 + (0- a sin theta + b cos theta
)^2)`
`= sqrt((a^2 (sin^2 theta + cos^2 theta ) + b^2 (sin^2 theta + cos^2 theta)`
But according to the trigonometric identity,
`sin^2 theta + cos^2 theta = 1`
Therefore,
`AB = sqrt(a^2 + b^2)`
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