If the polar coordinates of a point are $\left(2, \frac{\pi}{4}\right)$,then its Cartesian coordinates are

If the line joining the points $A(b \cos \alpha, b \sin \alpha)$ and $B(a \cos \beta, a \sin \beta)$ is extended to the point $N(x, y)$ such that $AN: NB = b: a$,then

Let $O(0, 0)$, $A(-1, 2)$ and $B(1, 3)$ be the vertices of $\Delta OAB$. The bisector of $\angle O$ intersects side $AB$ at point $D$. The value of $OD \cdot AB$ is equal to...

If $P, Q, R$ are collinear points such that $P(7, 7)$,$Q(3, 4)$ and $PR = 10$,then what are the coordinates of $R$?

In what ratio does the line $2x + 3y + 7 = 0$ divide the line segment joining the points $(3, 4)$ and $(7, 8)$?

The polar coordinate of a point $P$ is $\left(2, -\frac{\pi}{4}\right)$. The polar coordinate of the point $Q$, which is such that the line joining $PQ$ is bisected perpendicularly by the initial line, is