If x^2+y^2=a^2 and (x^2)/16+(y^2)/9=1 intersect at 4 points P,Q,R and S which form a square, then the area (in sq. units) of the square is

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MARKS Content Team · Accepted Answer

Correct answer: (D) 576/25. Let, P=acos⁡θ,asin⁡θ Then, acos⁡θ,asin⁡θ lies on (x^2)/16+(y^2)/9=1 Also, θ=45° because P,Q,R,S form a square ⇒(a^2)/(2×16)+(a^2)/(2×9)=1 ⇒(a^2)/2(16+9)/(16×9)=1⇒a^2=(2×144)/25 ⇒a=(12√2)/5⇒PQ=24/5 Hence, the area of the square=576/25

If $x^{2} + y^{2} = a^{2}$ and $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ intersect at $4$ points $P, Q, R$ and $S$ which form a square, then the area (in sq. units) of the square is

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More Ellipse Questions

If x2+y2=a2 and x216+y29=1 intersect at 4 points P,Q,R and S which form a square, then the area (in sq. units) of the square is

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More Ellipse Questions

If $x^{2} + y^{2} = a^{2}$ and $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ intersect at $4$ points $P, Q, R$ and $S$ which form a square, then the area (in sq. units) of the square is