The point of intersection of the tangents at the point P on the ellipse x2a2+y2b2=1,(a>b) and its corresponding point Q on the auxiliary circle, meet on the line
A
x=ae
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B
x=0
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C
y=0
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D
x=−ae
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Solution
The correct option is Cy=0
Tangent to the ellipse at point P(acosθ,bsinθ) is xacosθ+ybsinθ=1…(1)
Tangent to the circle at point Q(acosθ,asinθ) is xcosθ+ysinθ=a...(2)
The point of intersection of lines (1) and (2) is (acosθ,0), which lies on y=0.