If $p\,{\rm{and}}\,q$ are the lengths of the perpendiculars from the origin on the lines, $x\,\cos ec\,\alpha \, - \,y\,\sec \,\alpha \, = \,k\,\cot \,2\alpha \,{\rm{and}}\,x\,\sin \,\alpha \, + \,y\,\cos \,\alpha \, = \,k\,\sin \,2\alpha ,$ respectively then ${k^2}$ is equal to

JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

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Application +4 | -1

p\,\mathrm{and}\,q

are the lengths of the perpendiculars from the origin on the lines,

x\,\cos ec\,\alpha \, - \,y\,\sec \,\alpha \, = \,k\,\cot \,2\alpha \,\mathrm{and}\,x\,\sin \,\alpha \, + \,y\,\cos \,\alpha \, = \,k\,\sin \,2\alpha ,

respectively then

{k^2}

is equal to

View answer and explanation

Correct option: A

4{p^2} + {q^2}

Option D (

{p^2} + 4{q^2}

) is correct because by expressing p and q in terms of k and trigonometric functions, and then using the identity

{\sin^2} + {\cos^2} = 1

, we can derive the relationship

{k^2} = 4{p^2} + {q^2}