If the curves x2a2+y24=1 and y3=16x intersect at right angles, then a2=

AP EAMCET · Maths · Application of Derivatives

If the curves $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{4} = 1$ and $y^{3} = 16 x$ intersect at right angles, then $a^{2} =$

A $\frac{2}{3}$
B $\frac{2}{\sqrt{3}}$
C $\frac{4}{3}$
D $\frac{3}{4}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{4}{3}$

Step-by-step Solution

Detailed explanation

We have curves x2a2+y24=1 and y3=16x, Let, these two curves intersect at x1, y1 Slope of tangent at point x1, y1 in the curve x2a2+y24=1 y24=1-x2a2 ⇒ 2y4×dydx=-2xa2 ⇒ dydxx1, y1=m1x1, y1=-4x1y1a2 Slope of tangent at 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.

Same subject

Explore more questions on app

From AP EAMCET

Explore more questions on app