TS EAMCET · Maths · Parabola

The parametric equations of the parabola $x^{2} - 8 x + 12 y + 15 = 0$ are

A $x = 4 + 6 t, y = \frac{1}{12} - 3 t^{2}$
B $x = \frac{1}{12} - 3 t^{2}, y = 4 + 6 t$
C $x = 3 t^{2}, y = 6 t$
D $x = 6 t, y = 3 t^{2}$

Verified Solution

Answer & Solution

Correct Answer

(A) $x = 4 + 6 t, y = \frac{1}{12} - 3 t^{2}$

Step-by-step Solution

Detailed explanation

Given equation of parabola is x2-8x+12y+15=0 ⇒x2-8x+16=-12y-15+16 ⇒x-42=-12y-112 Compare it with x-h2=-4ay-k ⇒h=4,a=3, k=112 As, we know that the parametric equation of x-h2=-4ay is x=h+2at,y=k-at2. ∴Parametric equation of x-42=-12y-112 is…

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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The parametric equations of the parabola x2-8x+12y+15=0 are

Step-by-step Solution

The parametric equations of the parabola $x^{2} - 8 x + 12 y + 15 = 0$ are