TS EAMCET · Maths · Hyperbola

If the pole of the line $3 x - 16 y + 48 = 0$ with respect to the hyperbola $9 x^{2} - 16 y^{2} = 144$ is $(α, β),$ then $α - β =$

A $0$
B $- 3$
C $2$
D $- 7$

Verified Solution

Answer & Solution

Correct Answer

(C) $2$

Step-by-step Solution

Detailed explanation

Given: The pole of the line 3x-16y+48=0 with respect to the hyperbola 9x2-16y2=144 is α,β Equation of polar is given by T=0 ⇒9αx-16βy-144=0 These two lines are coinciding with each other ⇒9α3=-16β-16=-14448…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If the pole of the line 3x-16y+48=0 with respect to the hyperbola 9x2-16y2=144 is α,β, then α-β=

Step-by-step Solution

If the pole of the line $3 x - 16 y + 48 = 0$ with respect to the hyperbola $9 x^{2} - 16 y^{2} = 144$ is $(α, β),$ then $α - β =$