JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola

Statement \(-1\) : The slope of the tangent at any point \(P\) on a parabola, whose axis is the axis of \(x\) and vertex is at the origin, is inversely proportional to the ordinate of the point \(P\).
Statement \(-2\) : The system of parabolas \(y^2 = 4ax\) satisfies a differential equation of degree \(1\) and order \(1\)

A Statement \(- 1\) is true; Statement \(-2\) is true;
Statement \(-2\) is a correct explanation for statement \(- 1\)
B Statement \(- 1\) is true; Statement \(-2\) is true;
Statement \(-2\) is not a correct explanation for statement \(- 1\)
C Statement \(- 1\) is true; Statement \(-2\) is false
D Statement \(- 1\) is false; Statement \(-2\) is true

Verified Solution

Answer & Solution

Correct Answer

(B) Statement \(- 1\) is true; Statement \(-2\) is true;
Statement \(-2\) is not a correct explanation for statement \(- 1\)

Step-by-step Solution

Detailed explanation

statement- \(1\) : \({y^2} = \pm 4ax\) \( \Rightarrow \frac{{dy}}{{dx}} = \pm 2a.\frac{1}{y} \Rightarrow \frac{{dy}}{{dx}} \propto \frac{1}{y}\) Statememt-\(2\) : \({y^2} = 4ax \Rightarrow 2y\frac{{dy}}{{dx}} = 4a\) Thus both statements are true but statement- \(2\) is not a…

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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