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  • An ellipse slides between the two lines at right angles to one another. The locus of its centre is :Option: 1 Circle<div class='qna-opt

An ellipse slides between the two lines at right angles to one another. The locus of its centre is :

Option: 1

Circle


Option: 2

ellipse
 


Option: 3

parabola


Option: 4

hyperbola


Answers (1)

best_answer

Consider the perpendicular lines as X and Y axis .

Let co- ordinates of centre C be \mathrm{(\alpha, \beta)}

Hence equation of its director circle will be

\mathrm{ (x-\alpha)^2+(y-\beta)^2=a^2+b^2 }                           ....(2)
Considering the length of semimajor axis \mathrm{ =a}

and length of semi minor axis \mathrm{ =b}

Clearly (1) will pass through (0,0)

\mathrm{ \Rightarrow a^2+\beta^2=a^2+b^2 }
Hence required locus will be \mathrm{x^2+y^2=a^2+b^2.}

Posted by

Shailly goel

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