If the vertices and foci of a hyperbola are respectively ±3,0 and ±4,0 then the parametric equations of that hyperbola are

AP EAMCET · Maths · Hyperbola

If the vertices and foci of a hyperbola are respectively $(\pm 3, 0)$ and $(\pm 4, 0)$ then the parametric equations of that hyperbola are

A $x = 3 \sec θ, y = 7 \tan θ$
B $x = \sqrt{3} \sec θ, y = \sqrt{7} \tan θ$
C $x = \sqrt{3} \sec θ, y = 7 \tan θ$
D $x = 3 \sec θ, y = \sqrt{7} \tan θ$

Verified Solution

Answer & Solution

Correct Answer

(D) $x = 3 \sec θ, y = \sqrt{7} \tan θ$

Step-by-step Solution

Detailed explanation

Given, The vertices and foci of a hyperbola are respectively ±3,0 and ±4,0 So a=3 and ae=4, then e=43 Now we know that b2=a2e2-1 ⇒b2=32432-1 ⇒b2=16-9=7 ⇒b=7 So equation of hyperbola is given by x29-y27=1 Now parametric equation of hyperbola is given…

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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