MCQ
The equation ${x^2} - 16xy - 11{y^2} - 12x + 6y + 21 = 0$ represents
- AParabola
- BEllipse
- ✓Hyperbola
- DTwo straight lines
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$(a)$ reflection about the line $y=x$.
$(b)$ translation through $2$ units along the positive direction of $x$-axis.
$(c)$ rotation through angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction.
If the co-ordinates of the final position of the point $P$ are $\left(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$, then the value of $2 a+b$ is equal to: