The plane touches the surface only at point

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry

Problem

The plane 2x−2y+z+12=02x - 2y + z + 12 = 0 touches the surface x2+y2+z2−2x−4y+2z−3=0x^2 + y^2 + z^2 - 2x - 4y + 2z - 3 = 0 only at point (−1,λ,−2)(-1, \lambda, -2). The value of λ\lambda must be .....

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