AP EAMCET · Maths · Ellipse
If the line joining the points \(A(\alpha)\) and \(B(\beta)\) on the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) is a focal chord, then one possible value of \(\cot \frac{\alpha}{2} \cdot \cot \frac{\beta}{2}\) is
- A -3
- B 3
- C -9
- D 9
Answer & Solution
Correct Answer
(C) -9
Step-by-step Solution
Detailed explanation
Since equation of chord joining the points \(A(\alpha)\) and \(B(\beta)\) on the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) is \(\frac{x}{5} \cos \frac{\alpha+\beta}{2}+\frac{y}{3} \sin \frac{\alpha+\beta}{2}=\cos \frac{\alpha-\beta}{2}\) ...(i) \(\because\) Chord (i) is the…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The derivative of \(\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)\) with respect to \(\sqrt{1-x^2}\) at \(x=\frac{1}{2}\) equalsAP EAMCET 2021 Hard
- If a point \((a, a)\) falls between the lines \(|x+y|=4\), thenAP EAMCET 2021 Easy
- The number of solutions of the trigonometric equation \(1+\cos x \cdot \cos 5 x=\sin ^2 x\) in \([0,2 \pi]\) isAP EAMCET 2017 Medium
- \(\sqrt{12-\sqrt{68+48 \sqrt{2}}}\) is equal to :AP EAMCET 2006 Easy
- If the mean of a poisson distribution is \(\frac{1}{3}\), then the ratio \(P(X=1): P(X=2)\) isAP EAMCET 2021 Easy
- \(\int \frac{\sqrt{x^4+x^{-4}+2}}{x^3} d x=\)AP EAMCET 2023 Hard
More PYQs from AP EAMCET
- Let \(\overrightarrow{\mathrm{OA}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{OB}}=-2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}\) be the position vectors of two points \(A\) and \(B\). If \(C\) is a point on the bisector \(\angle \mathrm{AOB}\) and \(\mathrm{OC}=\sqrt{42}\), then \(\overrightarrow{\mathrm{OC}}=\)AP EAMCET 2023 Hard
- The value of the sum \(1 \times 2 \times 3+2 \times 3 \times 4+3 \times 4 \times 5+\ldots\) upto \(n\) terms is equal toAP EAMCET 2015 Hard
- The pair of gases responsible for acid rain areAP EAMCET 2012 Easy
- At \(27^{\circ} \mathrm{C}\), the osmotic pressure of a solution containing \(4 \mathrm{~g}\) of a non-electrolyte solute in \(1.0 \mathrm{~L}\) of solution is \(0.4 \mathrm{bar}\). The molar mass of the solute in \(\mathrm{g} \mathrm{mol}^{-1}\) is :
\(\left(\mathrm{R}=0.083 \mathrm{Lbar} \mathrm{K}^{-1} \mathrm{~mol}^{-1}\right)\)AP EAMCET 2017 Medium - One mole of fluorine is reacted with two moles of hot concentrated \(\mathrm{KOH}\). The products formed are \(\mathrm{KF}, \mathrm{H}_2 \mathrm{O}\) and \(\mathrm{O}_2\). The molar ratio of \(\mathrm{KF}, \mathrm{H}_2 \mathrm{O}\) and \(\mathrm{O}_2\), respectively isAP EAMCET 2002 Hard
- \(\lim _{x \rightarrow 0}\left(\frac{\sin a x}{\tan b x}\right)\) is equal toAP EAMCET 2021 Easy