Question
The ratio of the area enclosed by the locus of mid-point of PS and area of the ellipse where P is any point on the ellipse and S is the focus of the ellipse, is
Answer: Option D
:
D
x2a2+y2b2=1,Area=πabLetP=(acosθ,bsinθ)S=(ae,0)M(h,k)midpointofPS⇒h=ae+acosθ2;k=bsinθ2⇒(h−ae2a2)2+(kb2)2=1
Area = 14πab
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:
D
x2a2+y2b2=1,Area=πabLetP=(acosθ,bsinθ)S=(ae,0)M(h,k)midpointofPS⇒h=ae+acosθ2;k=bsinθ2⇒(h−ae2a2)2+(kb2)2=1
Area = 14πab
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