The area (in sq. units) of triangle formed by the tangent and normal at a point a2,b2 to the curve x2a2+y2b2=1 and X -axis is

AP EAMCET · Maths · Ellipse

The area (in sq. units) of triangle formed by the tangent and normal at a point $(\frac{a}{\sqrt{2}}, \frac{b}{\sqrt{2}})$ to the curve $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ and $X$ -axis is

A $\frac{a}{b} (a^{2} + b^{2})$
B $4 a b$
C $\frac{b}{4 a} (a^{2} + b^{2})$
D $2 a b$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{b}{4 a} (a^{2} + b^{2})$

Step-by-step Solution

Detailed explanation

We need to find the area of ∆PMN ar∆PMN=12×Length of normal×Length of tangent Now, x2a2+y2b2=1 ⇒dydx=-bxaa2-x2 Now, length of normal is given by =y1+dydx2 =b21+-bxaa2-x22 At x=a2 =b2aa2+b2 Now, length of tangent is given by…

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