45. Let $O ( 0,0 ) , P ( 3,4 ) , Q ( 6,0 )$ be the vertices of the triangle $O P Q$. The point $R$ inside the triangle $O P Q$ is such that the triangles $O P R , P Q R , O Q R$ are of equal area. The coordinates of $R$ are (A) $\left( \frac { 4 } { 3 } , 3 \right)$ (B) $\left( 3 , \frac { 2 } { 3 } \right)$ (C) $\left( 3 , \frac { 4 } { 3 } \right)$ (D) $\left( \frac { 4 } { 3 } , \frac { 2 } { 3 } \right)$ Answer ◯ [Figure][Figure][Figure] (A) (B) (C) (D)
A hyperbola, having the transverse axis of length $2 \sin \theta$, is confocal with the ellipse $3 x ^ { 2 } + 4 y ^ { 2 } = 12$. Then its equation is
45. Let $O ( 0,0 ) , P ( 3,4 ) , Q ( 6,0 )$ be the vertices of the triangle $O P Q$. The point $R$ inside the triangle $O P Q$ is such that the triangles $O P R , P Q R , O Q R$ are of equal area. The coordinates of $R$ are\\
(A) $\left( \frac { 4 } { 3 } , 3 \right)$\\
(B) $\left( 3 , \frac { 2 } { 3 } \right)$\\
(C) $\left( 3 , \frac { 4 } { 3 } \right)$\\
(D) $\left( \frac { 4 } { 3 } , \frac { 2 } { 3 } \right)$
Answer\\
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