AP EAMCET · Maths · Ellipse
The eccentricity of the ellipse \(9 x^2+5 y^2-18 x-20 y-16=0\), is :
- A \(\frac{1}{2}\)
- B \(\frac{2}{3}\)
- C \(\frac{3}{2}\)
- D 2
Answer & Solution
Correct Answer
(B) \(\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
Equation of ellipse is \(9 x^2+5 y^2-18 x-20 y-16=0\) \(\Rightarrow \quad 9\left(x^2-2 x\right)+5\left(y^2-4 y\right)=16\) \(\Rightarrow 9\left(x^2-2 x+1\right)+5\left(y^2-4 y+4\right)=16+9+20\) \(\Rightarrow \quad 9(x-1)^2+5(y-2)^2=45\)…
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
- If \(\frac{x-4}{x^2-5 x+6}\) can be expanded in the ascending powers of \(x\), then the coefficient of \(x^3\) isAP EAMCET 2004 Medium
- For the ellipse \(\frac{x^2}{18}+\frac{y^2}{32}=1\), if a tangent with slope \(\frac{-4}{3}\) intersects the major and minor axes at \(P\) and \(Q\) respectively. Find \(P\) and \(Q\).AP EAMCET 2020 Medium
- If the differential equation obtained by eliminating A,B from \(y=\left(\sin ^{-1} x\right)^2+A \cos ^{-1} x+B\) is \(\left(a-x^2\right) y^{\prime \prime}-x y^{\prime}=b\), then \(\frac{b+a}{b-a}=\)AP EAMCET 2022 Medium
- Let \(f: R \rightarrow R\) be defined by
\(f(x)=\left\{\begin{array}{ccc}\alpha+\frac{\sin [x]}{x}, & \text { if } & x>0 \\ 2, & \text { if } & x=0 \\ \beta+\left[\frac{\sin x-x}{x^3}\right], & \text { if } & x < 0\end{array}\right.\)
equal toAP EAMCET 2012 Easy - What is the quotient of \(x^3-5 x^2+2 x+7\) when divided with \((x-1)\) ?AP EAMCET 2020 Easy
- If power of a point \((4,2)\) with respect to the circle \(x^2+y^2\) \(-2 \alpha x+6 y+\alpha^2-16=0\) is 9 , then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes isAP EAMCET 2024 Medium
More PYQs from AP EAMCET
- The equation of the circle with \((1,1)\) as centre and which cuts a chord of length \(4 \sqrt{2}\) units on the line \(x+y+1=0\) isAP EAMCET 2017 Medium
- Which of the following has maximum coagulating power in the coagulation of positively charged sol?AP EAMCET 2024 Easy
- \(\int \frac{1-\cos x}{\cos x(1+\cos x)} d x=\)AP EAMCET 2023 Medium
- In how many ways can examination papers be arranged so that the best and the worst papers are never together?AP EAMCET 2021 Easy
- The work done in rotating a bar magnet which is initially in the direction of a uniform magnetic field through \(45^{\circ}\) is W. The additional work to be done to rotate the magnet further through \(15^{\circ}\) isAP EAMCET 2025 Medium
- For \(n \geq 2\), If \(I_n=\int \sec ^n x d x\), then \(I_4-\frac{2}{3} I_2=\)AP EAMCET 2018 Hard