AP EAMCET · Maths · Straight Lines

The point to which the origin should be shifted in order to eliminate the $x$ and $y$ terms from the equation $9 x^{2} + 4 y^{2} + 10 x + 12 y + 1 = 0$ is

A $(\frac{5}{9}, \frac{3}{2})$
B $(\frac{- 5}{2}, \frac{- 3}{9})$
C $(\frac{- 5}{9}, \frac{- 3}{2})$
D $(\frac{- 3}{2}, \frac{- 5}{9})$

Verified Solution

Answer & Solution

Correct Answer

(C) $(\frac{- 5}{9}, \frac{- 3}{2})$

Step-by-step Solution

Detailed explanation

Let the origin be shifted at h,k Let x',y' be the new co-ordinate ∴ x=x'+h & y=y'+k ∵ Given equation is 9x2+4y2+10x+12y+1=0 Put x=x'+h & y=y'+k ⇒ 9x'+h2+4y'+k2+10x'+h+12y'+k+1=0…

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 point to which the origin should be shifted in order to eliminate the x and y terms from the equation 9x2+4y2+10x+12y+1=0 is

Step-by-step Solution

The point to which the origin should be shifted in order to eliminate the $x$ and $y$ terms from the equation $9 x^{2} + 4 y^{2} + 10 x + 12 y + 1 = 0$ is