TS EAMCET · Maths · Ellipse
Assertion (A): The image of \(\frac{x^2}{25}+\frac{y^2}{16}=1\) in the line \(x+y=10\) is \[ \frac{(x-10)^2}{16}+\frac{(y-10)^2}{25}=1 \text {. } \] Reason (R): The image of a curve ' \(\mathrm{C}\) ' in a line \(\mathrm{L}\) is the locus of the image of every point of \(\mathrm{C}\) with respect to the line \(\mathrm{L}\). The correct option among the following is:
- A (A) is true, (R) is true and (R) is the correct explanation for (A)
- B (A) is true, (R) is true but (R) is not the correct explanation for (A)
- C (A) is true but (R) is false
- D (A) is false but (R) is true
Answer & Solution
Correct Answer
(A) (A) is true, (R) is true and (R) is the correct explanation for (A)
Step-by-step Solution
Detailed explanation
Given equation of ellipse is \(\frac{x^2}{25}+\frac{y^2}{16}=1\) The image of the ellipse in the line \(x+y-10\) will be \(\frac{(x-h)^2}{16}+\frac{(y-k)^2}{25}=1\) Centre of original equation is \((0,0)\) and other equation is \((h, k)\) Midpoint is…
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 range of the real valued function \(f(x)=\frac{1}{x-|x|}\) isTS EAMCET 2023 Easy
- \(\text { If } \frac{2 x^2-3 x+5}{(x-7)^3}=\frac{\mathrm{A}}{x-7}+\frac{\mathrm{B}}{(x-7)^2}+\frac{\mathrm{C}}{(x-7)^3}\) then \(2 \mathrm{~A}-3 \mathrm{~B}+\mathrm{C}=\)TS EAMCET 2022 Easy
- \(\mathbf{a}=\mathbf{i}+\mathbf{j}-2 \mathbf{k} \Rightarrow \sum\{(\mathbf{a} \times \mathbf{i}) \times \mathbf{j}\}^2\) is equal toTS EAMCET 2012 Easy
- If thenTS EAMCET 2021 Medium
- Let \(f(x)=\sin x, g(x)=\cos x, h(x)=x^2\) then \(\lim _{x \rightarrow 1} \frac{f(g(h(x)))-f(g(h(1)))}{x-1}=\)TS EAMCET 2022 Easy
- The total number of all those 3-digit numbers in which the sum of all the digits in each of them is 10 , isTS EAMCET 2023 Hard
More PYQs from TS EAMCET
- At \(T(K)\) the equilibrium constants for the following two reactions are given below \(\begin{aligned} & 2 \mathrm{~A}(\mathrm{~g}) \rightleftharpoons \mathrm{B}(\mathrm{~g})+\mathrm{C}(\mathrm{~g}) ; \mathrm{K}_1=16 \ & 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{D}(\mathrm{~g}) ; \mathrm{K}=25 \end{aligned}\)
What is the value of equilibrium constant ( K ) for the reaction given below at \(\mathrm{T}(\mathrm{K})\) ? \(\mathrm{A}(\mathrm{~g})+\frac{1}{2} \mathrm{~B}(\mathrm{~g}) \rightleftharpoons \mathrm{D}(\mathrm{~g})\)TS EAMCET 2024 Medium - If the ratio of the mass numbers of two nuclei is \(27: 125\), then the ratio of their surface areas isTS EAMCET 2025 Medium
- In an \(n\)-type semiconductor, electrons are majority charge carriers and holes are minority charge carriers. The charge of an \(n\)-type semiconductor isTS EAMCET 2024 Easy
- Given that \(\mathrm{N}_2(g)+3 \mathrm{H}_2(g) \longrightarrow 2 \mathrm{NH}_3(g)\); \(\Delta_r H^{\circ}=-92 \mathrm{~kJ}\), the standard molar enthalpy of formation in \(\mathrm{kJ} \mathrm{mol}^{-1}\) of \(\mathrm{NH}_3(g)\) isTS EAMCET 2016 Easy
- The number of and carbon in Hepta--dien- -yne, respectively, areTS EAMCET 2021 Medium
- In the figure, the chamber A contains a gas, movable chamber B is placed on the top of the gas and it contains \(\mathrm{n}\) metal balls. The weight of chamber B is supported by the gas. Chamber \(\mathrm{C}\) has vacuum. Let the gas be in equilibrium at pressure \(\mathrm{P}\). Let \(\mathrm{P}^{\prime}\) be the pressure if one of the balls is taken away. Find \(\left(\mathrm{P}-\mathrm{P}^{\prime}\right) / \mathrm{P}\).
TS EAMCET 2022 Hard