If tanθ1×tanθ2=-a2b2, then the chord joining 2 points θ1 and θ2 on the ellipse x2a2+y2b2=1 will subtend a right angle at

AP EAMCET · Maths · Ellipse

If $\tan θ_{1} \times \tan θ_{2} = \frac{- a^{2}}{b^{2}}$ , then the chord joining $2$ points $θ_{1}$ and $θ_{2}$ on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ will subtend a right angle at

A Focus
B Center
C end of major axis
D end of minor axis

Verified Solution

Answer & Solution

Correct Answer

(B) Center

Step-by-step Solution

Detailed explanation

Let the two points be Aacosθ1,bsinθ1 & Bacosθ2,bsinθ2 O0,0 is origin Slope of OA=bsinθ1acosθ1=btanθ1a Slope of OB=bsinθ2acosθ2=btanθ2a Slope of OA×Slope of OB=b2a2tanθ1tanθ2=-1 Therefore, chord…

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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