AP EAMCET · Maths · Ellipse
If the ellipse \(4 x^2+9 y^2=36\) is confocal with a hyperbola whose length of the transverse axis is 2 , then the points of intersection of the ellipse and hyperbola lie on the circle
- A \(x^2+y^2=81\)
- B \(x^2+y^2=16\)
- C \(x^2+y^2=25\)
- D \(x^2+y^2=5\)
Answer & Solution
Correct Answer
(D) \(x^2+y^2=5\)
Step-by-step Solution
Detailed explanation
Ellipse : \(4 x^2+9 y^2=36\) ....(i) and Hyperbola \(=\frac{x^2}{1}-\frac{y^2}{b^2}=1\) \(\Rightarrow b^2 x^2-y^2=b^2\) As, they are confocal \(\therefore(a e)^2=a^2+b^2 \Rightarrow 5=1+b^2 \Rightarrow b^2=4\) So, hyperbola \(4 x^2-y^2=4\) .....(ii) Adding (i) and (ii),…
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
- \(\int \frac{\sqrt{\cot x}}{\sin x \cos x} d x=-f(x)+c \Rightarrow f(x)\)AP EAMCET 2004 Easy
- The sum of squares of roots of the equation \(x^{\frac{2}{3}}+x^{\frac{1}{3}}-2=0\) isAP EAMCET 2022 Easy
- If \(x+y-1=0\) and \(2 x-y+1=0\) are conjugate lines with respect to a circle \(x^2+y^2-4 x+2 f y-1=0\), then \(f=\)AP EAMCET 2023 Medium
- If \(\mathbf{P}=3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{Q}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) are two sides of a triangle, then its area is equal to ____ sq units.AP EAMCET 2020 Easy
- If \(\frac{x^4}{(x-1)(x-2)}=f(x)+\frac{A}{x-1}+\frac{B}{x-2}\), then \(f(-2)+A+B=\)AP EAMCET 2025 Medium
- The angle between the lines with direction ratios and isAP EAMCET 2020 Easy
More PYQs from AP EAMCET
- The equation of a normal to the circle \(x^2+y^2-2 x=0\) that is parallel to the line \(x+2 y-\) \(3=0\) isAP EAMCET 2020 Medium
- \(\int_{\frac{1}{25}}^3 \frac{e^{\frac{3}{x}}}{x^2} d x=\)AP EAMCET 2023 Easy
- The coefficient of mutual inductance between the primary and the secondary coil of a transformer is \(0.2 \mathrm{H}\). When the current in the primary changes by \(5 \mathrm{As}^{-1}\), then the induced emf in the secondary will beAP EAMCET 2020 Hard
- A \(40 \% \mathrm{HCl}\) solution has density \(1.2 \mathrm{~g} \mathrm{~mL}^{-1}\). The molarity of the solution is nearly ____AP EAMCET 2020 Easy
- In a closed organ pipe, the number of nodes formed in fifth and ninth harmonics are respectivelyAP EAMCET 2025 Easy
- Assertion (A) Propene on addition with hydrogen bromide in the presence of peroxide gives 1-bromopropane as the major product.
Reason (R) l-bromopropane is the major product because it is formed through the stable carbocation.
The correct answer isAP EAMCET 2018 Easy