Question

The point of contact of the plane $2x-2y+z+12=0$ and sphere $x^2+y^2+z^2-2x-4y+2z-3=0$ is

• A. $(1,4,3)$
• B. $(3,4,1)$
• C. $(-1,-4,2)$
• D. $(-1,4,-2)$

Answer 1

The correct option is D $(-1,4,-2)$

Let the point be $P(a,b,c)$

So equation of tangent to the given sphere at $P$ is given by,

$ax+by+cz-1(x+a)-2(y+b)+1(z+c)-3=0$

$\Rightarrow (a+1)x+(b-2)y+(c+1)z+(c-a-2b-3)=0$ (i)

Now comparing (i) with the given tangent, $2x-2y+z+12=0$

$\frac{a+1}{2}=\frac{b-2}{-2}=\frac{c+1}{1}=\frac{c-a-2b-3}{12}$

Solving these equation, we get required point of contact $(-1,4,-2)$.