TS EAMCET · Maths · Ellipse

For the ellipse $4 {(x - 2 y + 1)}^{2} + 9 {(2 x + y + 2)}^{2} = 25,$ which of the following is true?

A equation of major axis is $x - 2 y + 1 = 0$
B eccentricity $\frac{\sqrt{5}}{2}$
C length of major axis is $\frac{1}{2} \sqrt{5}$
D centre is $(1, 0)$

Verified Solution

Answer & Solution

Correct Answer

(A) equation of major axis is $x - 2 y + 1 = 0$

Step-by-step Solution

Detailed explanation

Given, 4x-2y+12+92x+y+22=25 x-2y+1214+2x+y+2219=12+222 ...1 Here, Equation of major axis x-2y+1=0 ...2 And equation of minor axis is 2x+y+2=0 ...3 Centre is the point of intersection of 2 & 3. ∴Equation 3-equation2×2, we…

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.

Same subject

Explore more questions on app

From TS EAMCET

Explore more questions on app

For the ellipse 4x-2y+12+92x+y+22=25, which of the following is true?

Step-by-step Solution

For the ellipse $4 {(x - 2 y + 1)}^{2} + 9 {(2 x + y + 2)}^{2} = 25,$ which of the following is true?