A) circle circumscribing the \[\Delta PQR\] passes through the vertex of the parabola.
B) the algebraic sum of slopes of the tangents at P, Q and R vanishes.
C) the algebraic sum of the ordinates of the points P vanishes.
D) circumcentre of \[\Delta PQR\] lies on the axis of the parabola.
Correct Answer: A
Solution :
Since, the line \[\frac{x}{e}+\frac{y}{e'}=1\] touches the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]. \[\therefore \] \[\frac{1}{\sqrt{\frac{1}{{{e}^{2}}}+\frac{1}{e{{'}^{2}}}}}=2\] \[\Rightarrow \] \[a=\frac{ee'}{\sqrt{{{e}^{2}}+e{{'}^{2}}}}=2\] [from Eq. (i)]
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