Conic Sections Question 301
Question: The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $ \frac{x^{2}}{9}+\frac{y^{2}}{5}=1 $ , is
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Options:
A) 27/4 sq. unit
B) 9 sq. unit
C) 27/2 sq. unit
D) 27 sq. unit
Show Answer
Answer:
Correct Answer: D
Solution:
By symmetry the quadrilateral is a rhombus. So area is four times the area of the right angled triangle formed by the tangent and axes in the Ist quadrant. Now, $ ae=\sqrt{a^{2}-b^{2}}\Rightarrow ae=2 $
therefore Tangent (in first quadrant) at end of latus rectum $ ( 2,\frac{5}{3} ) $ is $ \frac{2}{9}x+\frac{5}{3}\frac{y}{5}=1 $ i.e., $ \frac{x}{9/2}+\frac{y}{3}=1 $
Area $ =4.\frac{1}{2}.\frac{9}{2}.3=27 $ sq. unit.
BETA
