Question

p₁, p₂ are lengths of perpendicular from foci on tangent to ellipse and p₃, p₄ are perpendiculars from extremities of major axis and p from centre of ellipse on same tangent, then $\frac{p_{1}p_{2} - p^{2}}{p_{3}p_{4} - p^{2}}$ equals

• A. e
• B. $\sqrt{e}$
• C. e²
• D. None of these

Answer 1

Answer: (C)

e²

Answer 2

Let tangent is y = mx + c

\ p = $\frac{c}{\sqrt{m^{2} + 1}}$, p₁ = $\left| \frac{c + aem}{\sqrt{1 + m^{2}}} \right|$,

p₂ = $\frac{|c–aem|}{\sqrt{1 + m^{2}}}$, p₃ = $\frac{|am + c|}{\sqrt{1 + m^{2}}}$,

p₄ = $\frac{|c–am|}{\sqrt{1 + m^{2}}}$

Now put values in $\frac{p_{1}p_{2} - p^{2}}{p_{3}p_{4} - p^{2}}$