Question

find the equation to the core whose vertex is the point (a,b,c) and whose generating line intersects the conic px2+qy2 = 1,z=0​

Answer 1

p (az - cx)² + q (bz - cy)² = (z - c)²

Step-by-step explanation:

The guiding curve is

px² + qy² = 1, z = 0

Let, the straight line through (a, b, c) be

(x - a) / l = (y - b) / m = (z - c) / n ..... (1)

This line meets the plane z = 0

Then, (x - a) / l = (y - b) / m = - c / n ... (1)

This gives

x = a - cl/n , y = b - cm/n

The point (a - cl/n, b - cm/n, 0) lies on the curve px² + qy² = 1, then

p (a - cl/n)² + q (b - cm/n)² = 1

or, p (an - cl)² + q (bn - cm)² = n²

or, p {a (z - c) - c (x - a)}² + q {b (z - c) - c (y - b)}² = (z - c)²

or, p (az - cx)² + q (bz - cy)² = (z - c)² ,

which is the equation of the required cone.

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Find the equation to the cone whose vertex is the point (a,b,c) and whose generating lines intersects the conic px2 + qy2 = 1, z = 0. - https://brainly.in/question/12257434