{\A}( {\a}, 0) is a fixed point and \theta is a parameter such that 0< \theta< 2 \pi. If {\P}( {\a} \cos \theta, {\a} \sin \theta) is a point on the circle {\x}^2+ {\y}^2= {\a}^2 and {\Q}( {\b} \sin \theta,- {\b} \cos \theta) is a point on the circle x^2+y^2=b^2, then the locus of the centroid of the triangle APQ is [AP EAPCET 24 May 2025 S1]

Correct Answer is : a circle with centre at (a3,0) and radius (√a2+b23)

a circle with centre at (\frac{ {\a}}{3}, 0) and radius ( \sqrt{ {\a}^2+ {\b}^2}}/{3})

a circle with centre at (a, 0) and radius ( {\sqrt{a^2+b^2}}/{3})

a parabola with focus at (\frac{a}{3}, 0)

a parabola with focus at (a, 0)

Circle

Section: Mathematics

Question : 16 of 89

Marks: +1, -0

A(a,0) is a fixed point and θ is a parameter such that 0<θ<2π. If P(a‌cos‌θ,asin‌θ) is a point on the circle x2+y2=a2 and Q(bsin‌θ,−b‌cos‌θ) is a point on the circle x2+y2=b2, then the locus of the centroid of the triangle APQ is

[AP EAPCET 24 May 2025 S1]

a circle with centre at (‌
a
3
,0) and radius (‌
√a2+b2
3
)
a circle with centre at (a,0) and radius (‌
√a2+b2
3
)
a parabola with focus at (‌
a
3
,0)
a parabola with focus at (a,0)

Validate

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