Amit M Agarwal Solutions for Chapter: Three Dimensional Geometry, Exercise 6: Target Exercises

The equation of the sphere with centre $(3,6,-4)$ and touching the plane $2x-2y-z-10=0,$ is

The equation $x^2+y^2+z^2-4x+6y-8z+29=0$ represents

The centre of the sphere $x\left(x-x_1\right)+y\left(y-y_1\right)+z\left(z-z_1\right)=0$ is

The position vector of the centre of the sphere ${\left|\overrightarrow{r}\right|}^2+\overrightarrow{r}·\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}\right)-9=0$ is

The equation of the sphere circumscribing the tetrahedron whose faces are $x=0, y=0, z=0$ and $\frac{x}{a}+\frac{y}{a}+\frac{z}{a}=1$, is

The equation of the sphere whose centre is at origin and which touches the plane $\overrightarrow{r}·\hat{\mathrm{n}}=p,$ is

A sphere through non-collinear points $A,B$ and $C$ are smallest when its centre is

There is one and only one sphere passing through