Question

Find equation of the right circular cone whose vertes is P(2, -3,5),axis PQ which makes equil angles with the axis and which passes through A(1,-2,3)

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given: P(2,-3,5)

          PQ passes through A(1,-2,3)

To find: The right circular cone equation

Find:

Vertices of the cone are ( 2,-3, 5)

Direction cosines of its generators to satisfy the equation l² + 2m² - 3n²=0 -----eq1

Axis passes through A (1,-2,3)

(x-x1)/l = (y-y1)/m=(z-z1)/n = r

(2-1)/l = (-3 - (-2))/m= (5 - 3)/n = r ------eq2

After solving eq 2, we get

l= 1/r ; m = -1/r ; n = 2/r

Substitute the value of l,m, and n in eq1

(1/r)² + 2(-1/r)² -3(2/r)² = 0

The equation for the right circular cone is (1/r)² + 2(-1/r)² -3(2/r)² = 0