AP EAMCET · Maths · Ellipse
If the eccentric angles of the extremeties of a focal chord (other than the major axis) of the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) are \(\alpha\) and \(\beta\) then \(\frac{\cot \left(\frac{\alpha}{2}\right)}{\tan \left(\frac{\beta}{2}\right)}=\)
- A \(\frac{4}{3}\)
- B -9
- C 9
- D \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(B) -9
Step-by-step Solution
Detailed explanation
\( a^2=25, b^2=9 \) \( e = \sqrt{1 - \frac{b^2}{a^2}} = \sqrt{1 - \frac{9}{25}} = \frac{4}{5} \) \( \tan \left(\frac{\alpha}{2}\right) \tan \left(\frac{\beta}{2}\right) = \frac{e-1}{e+1} = \frac{\frac{4}{5}-1}{\frac{4}{5}+1} = -\frac{1}{9} \)…
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
- \(\int \frac{\sin (x-a)}{\sin (x-b)} d x=A x+B \log |\sin (x-b)|+C \Rightarrow(A, B)=\)AP EAMCET 2017 Hard
- If , thenAP EAMCET 2021 Medium
- The circumcentre of the triangle formed by the points \(A(1, \sqrt{3}), B(-1,-\sqrt{3})\) and \((3,-\sqrt{3})\) isAP EAMCET 2021 Easy
- For \(n \in N\), if \(I_n=\int \frac{\sin n x}{\sin x} d x=\frac{2}{n-1} \sin (n-1) x+I_{n-2}\) and \(\int_0^\pi \frac{\sin n x}{\sin x} d x=\frac{k \pi}{2}\), then \(k=\)AP EAMCET 2022 Medium
- If \(x>0, x^y=e^{x-y}\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2004 Medium
- \(\int_0^1 \sqrt{\frac{2+x}{2-x}} d x=\)AP EAMCET 2024 Hard
More PYQs from AP EAMCET
- If \(-2, \frac{4}{3}, \frac{-4}{5}\) are the intercepts made by a plane on \(\mathrm{X}, \mathrm{Y}, \mathrm{Z}\)-axes respectively then the direction cosines of a normal to this plane areAP EAMCET 2022 Easy
- Compounds of alkaline earth metals are less soluble in water than the corresponding alkali metal compounds due toAP EAMCET 2017 Easy
- Two towns \(A\) and \(B\) are connected by a regular bus service with a bus leaving in either direction every \(T\) min. A man cycling with a speed of \(20 \mathrm{~km} / \mathrm{h}\) from \(A\) to \(B\) notices that a bus travelling in the direction of his motion goes past him every \(18 \mathrm{~min}\) and every \(6 \mathrm{~min}\) he notices a bus travelling in the opposite direction go past him. Assuming that, the buses travel with a constant speed. Find \(T\) and the constant speed of the buses.AP EAMCET 2021 Medium
- The length of the tangent drawn from any point on the circle \(x^2+y^2+2 g x+2 f y+c_1=0\) to the circle \(x^2+y^2+2 g x+2 f y+c_2=0\) isAP EAMCET 2020 Easy
- Two water pipes of diameter \(2 \mathrm{~cm}\) and \(4 \mathrm{~cm}\) are separately connected to a main supply line. The velocity of flow of water in the pipe of \(2 \mathrm{~cm}\) diameter isAP EAMCET 2020 Medium
- Below shown molecules are
AP EAMCET 2023 Easy