TS EAMCET · Maths · Ellipse
If the straight line \(8 x+3 \sqrt{2} y=36\) touches the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=2\) at \((a, b)\), then \(a+\sqrt{2} b=\)
- A \(\frac{36}{5 \sqrt{2}}\)
- B \(\frac{8}{3}\)
- C \(\frac{12+2 \sqrt{2}}{3}\)
- D \(\frac{16}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{16}{3}\)
Step-by-step Solution
Detailed explanation
Given, \(8 x+3 \sqrt{2} y=36\) \( \frac{x^2}{9}+\frac{y^2}{4}=2,(a, b) \) \( \begin{gathered} \frac{x x_1}{9}+\frac{y y_1}{4}-2=0 \\ 8 x+3 \sqrt{2} y-36=0 \end{gathered} \) Eqs. (i) and (ii) represents same line, so…
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 circle \(4 x^2+4 y^2-12 x-12 y+9=0\)TS EAMCET 2013 Medium
- If \(P(A \cup B)=0.8\) and \(P(A \cap B)=0.3\), then \(P\left(A^C\right)+P\left(B^C\right)\) is equal toTS EAMCET 2021 Easy
- The length of the common chord of the two circles \(x^2+y^2-4 x-8 y+4=0\) and \(x^2+y^2-8 x-12 y+16=0\) isTS EAMCET 2022 Medium
- \(A\) is a singular matrix of order five. \(B\) is another matrix having the \(\operatorname{rank} \rho(B)\) equal to the rank \(\rho(A)\) and \(B\) has a non-zero minor of order 3. Then which one of the following is true?TS EAMCET 2020 Easy
- A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of getting 4 heads, then the probability of getting 6 heads isTS EAMCET 2024 Medium
- If \(m\) and \(M\) respectively denote the minimum and maximum of \(f(x)=(x-1)^2+3\) for \(x \in[-3,1]\), then the ordered pair \((m, M)\) is equal toTS EAMCET 2008 Easy
More PYQs from TS EAMCET
- The number of points \(z\) on the Argand plane which satisfy the conditions \(\operatorname{Re}\left(\frac{z-2}{z-4 i}\right)=0\) and \(\lim \left(\frac{z-2}{z-4 i}\right)=1\) simultaneously isTS EAMCET 2020 Medium
- \(\lim _{n \rightarrow \infty} \frac{(2 n(2 n-1) \ldots(n+2)(n+1))^{1 / n}}{n}=\)TS EAMCET 2025 Hard
- The nuclear forces areTS EAMCET 2020 Easy
- Consider the equilibrium, \(\mathrm{H}_2+\mathrm{I}_2 \rightleftharpoons 2 \mathrm{HI}\). Calculate the equilibrium constant of the reverse reaction when the equilibrium concentration of \(\mathrm{H}_2, \mathrm{I}_2\) and \(\mathrm{HI}\) are \(1.14 \times 10^{-2}, 0.12 \times 10^{-2}\) and \(2.52 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}\), respectivelyTS EAMCET 2019 Easy
- Match the values of \(\frac{d y}{d x}\) at \(x=\frac{\pi}{3}\) for the following system of curves in parametric form given in List-I with those of the items in List-II
TS EAMCET 2023 Easy - Let \(z=x+i y\) represent a point \(\mathrm{P}(x, y)\) in the Argand plane. If \(z\) satisfies the condition that amplitude of \(\frac{z-3}{z-2 i}=-\frac{\pi}{2}\), then the locus of P isTS EAMCET 2025 Medium