A) focus
B) centre
C) end of the major axis
D) end of the minor axis
Correct Answer: B
Solution :
Let \[P(a\cos {{\theta }_{1}},b\sin {{\theta }_{1}})\] and\[Q(a\cos {{\theta }_{2}},b\sin {{\theta }_{2}})\] be two points on the ellipse. Then, \[{{m}_{1}}=\]slope of\[OP=\frac{b}{a}\tan {{\theta }_{1}}\] and \[{{m}_{2}}=\]slope of \[OQ=\frac{b}{a}\tan {{\theta }_{2}}\] \[\therefore \] \[{{m}_{1}}{{m}_{2}}=\frac{{{b}^{2}}}{{{a}^{2}}}\tan {{\theta }_{1}}\tan {{\theta }_{2}}\] \[=\frac{{{b}^{2}}}{{{a}^{2}}}\times \frac{-{{a}^{2}}}{{{b}^{2}}}\] \[\left[ \therefore \tan {{\theta }_{1}}\tan {{\theta }_{2}}=-\frac{{{a}^{2}}}{{{b}^{2}}}(given) \right]\] \[=-1\] \[\therefore \] \[\angle POQ=\frac{\pi }{2}\] Hence, PQ makes a right angle at the centre of the ellipse.You need to login to perform this action.
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