If the straight line intersect the curve

MATHEMATICS · Subjective · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

If the straight line x−αl=y−βm=z−γn\frac{x-\alpha}{l} = \frac{y-\beta}{m} = \frac{z-\gamma}{n} intersect the curve ax2+by2=1,z=0ax^2 + by^2 = 1, z = 0 , then prove that a(αn−γl)2+b(βn−γm)2=n2a(\alpha n - \gamma l)^2 + b(\beta n - \gamma m)^2 = n^2 .

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