A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point :

Let $$\alpha $$ $$ \in $$ R and the three vectors

$$\overrightarrow a = \alpha \widehat i + \widehat j + 3\widehat k$$, $$\overrightarrow b = 2\widehat i + \widehat j - \alpha \widehat k$$

and $$\overrightarrow c = \alpha \widehat i - 2\widehat j + 3\widehat k$$.

Then the set S = {$$\alpha $$ : $$\overrightarrow a $$ , $$\overrightarrow b $$ and $$\overrightarrow c $$ are coplanar} :

If [x] denotes the greatest integer $$ \le $$ x, then the system of linear equations [sin $$\theta $$]x + [–cos$$\theta $$]y = 0, [cot$$\theta $$]x + y = 0

The tangents to the curve y = (x – 2)² – 1 at its points of intersection with the line x – y = 3, intersect at the point :