CUET · MATHS · PYQ PAPER 2023

The equation of the curve whose slope is given by \(\frac{d y}{d x}=\frac{4 x}{y}, x>0, y>0\) and which passes through the point \((2,2)\) is:

A \(y^2=4 x^2-12\)
B \(x^2=4 y^2-12\)
C \(y^2=4 x^2+12\)
D \(x^2=4 y^2+12\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(y^2=4 x^2-12\)

Step-by-step Solution

Detailed explanation

\(y \, dy = 4x \, dx\) \(\int y \, dy = \int 4x \, dx\) \(\frac{y^2}{2} = 2x^2 + C\) \(y^2 = 4x^2 + C'\) \(2^2 = 4(2^2) + C'\) \(4 = 16 + C'\) \(C' = -12\) \(y^2 = 4x^2 - 12\)

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 CUET

Explore more questions on app

List-I	List-II
(A) Gamma rays	(I) 1nm to \(10^{-3}nm\)
(B) Microwaves	(II) 1mm to 700nm
(C) X-rays	(III) \(< 10^{-3}nm\)
(D) Infrared waves	(IV) 10mm to 1mm