Question
The area of quadrilateral formed by tangents at the ends of latus-rectum of the ellipse x2 + 2y2 = 2 is-
- 8
- 8
- None of these
Hint:
find the end points of latus rectum and find the equations of tangents. find the x and y intercepts of these tangents and find out the area.
The correct answer is:
equation of ellipse : x2+2y2=2
a2=2, b2= 1,e2=1-1/2=1/2
ends of latus rectum = (±ae, ±b2/a)
equation of tangent at (1,1/√2) :
x+√2y=2
x intercept of this tangent: x=2
y intercept : √2
area of this triangle = ½ x 2 x √2 = √2
total area of quadrilateral = 4 x √2 = 4√2 sq units
the tangents are symmetrical about the origin. hence, the area of one of the triangles can be multiplied by 4 to get the total area.
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