AP EAMCET · Maths · Ellipse
The equation of the locus of a point \((2 \cos \theta-3,3 \sin \theta-4)\) is
- A \(9 x^2+4 y^2+54 x+32 y+181=0\)
- B \(4 x^2+9 y^2+54 x+32 y+109=0\)
- C \(9 x^2+4 y^2-54 x+32 y+109=0\)
- D \(9 x^2+4 y^2+54 x+32 y+109=0\)
Answer & Solution
Correct Answer
(D) \(9 x^2+4 y^2+54 x+32 y+109=0\)
Step-by-step Solution
Detailed explanation
Given point \((2 \cos \theta-3,3 \sin \theta-4)=(x, y)\) Let…
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
- For \(k=1,2,3\) the box \(B_k\) contains \(k\) red balls and \((k+1)\) white balls. Let \(P\left(B_1\right)=\frac{1}{2}\), \(P\left(B_2\right)=\frac{1}{3}\) and \(P\left(B_3\right)=\frac{1}{6}\). A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box \(B_2\), isAP EAMCET 2008 Medium
- The triangle \(P Q R\) is inscribed in the circle \(x^2+y^2=25\). If \(\mathrm{Q}=(3,4)\) and \(\mathrm{R}=(-4,3)\) then \(\angle \mathrm{QPR}=\)AP EAMCET 2024 Easy
- Find the coefficient of \(x^5\) in \(\left(1+x+x^2\right)^8\).AP EAMCET 2020 Easy
- If \(\int \frac{\mathrm{dx}}{1-\sin ^4 \mathrm{x}}=\mathrm{A} \tan \mathrm{x}+\mathrm{B} \operatorname{Tan}^{-1}(\sqrt{2} \tan \mathrm{x})+\mathrm{C}\), then \(\mathrm{A}^2-\mathrm{B}^2=\)AP EAMCET 2025 Hard
- The length of the normal to the curve \(x=a(\theta+\sin \theta), y=a(1-\cos \theta)\) at \(\theta=\frac{\pi}{2}\) isAP EAMCET 2017 Medium
- The differential equation formed by eliminating arbitrary constants \(\mathrm{A}, \mathrm{B}\) from the equation \(y=A \cos 3 x+\mathrm{B} \sin 3 x\) isAP EAMCET 2024 Easy
More PYQs from AP EAMCET
- If \(p\) th, \(q\) th, \(r\) th terms of a geometric progression are the positive numbers \(a, b\) and \(c\) respectively, then the angle between the vectors \(\left(\log a^2\right) \mathbf{i}+\left(\log b^2\right) \mathbf{j}+\left(\log c^2\right) \mathbf{k} \quad\) and \((q-r) \mathbf{i}+(r-p) \mathbf{j}+(p-q) \mathbf{k}\) isAP EAMCET 2012 Hard
- A uniform chain of length \(L\) is lying on the horizontal table. If the coefficient of friction between the chain and the table top is \(\mu\), what is the maximum length of the chain that can hang over the edge of the table without disturbing the rest of the chain on the table?AP EAMCET 2011 Hard
- Three moles of a gas at a temperature ' \(\mathrm{T}\) ' is heated to thrice its volume by keeping the pressure constant. If ' \(\gamma\) is the ratio of specific heats, then the increase in internal energy of the gas isAP EAMCET 2023 Medium
- \(1+\frac{1+2}{2 !}+\frac{1+2+2^2}{3 !}+\ldots\) is equal toAP EAMCET 2002 Medium
- \(f(x)\) and \(g(x)\) are differentiable functions such that \(\frac{f(x)}{g(x)}=\) a non zero constant. If \(\frac{\mathrm{f}^{\prime}(\mathrm{x})}{\mathrm{g}^{\prime}(\mathrm{x})}=\alpha(\mathrm{x})\) and \(\left(\frac{\mathrm{f}(\mathrm{x})}{\mathrm{g}(\mathrm{x})}\right)^{\prime}=\beta(\mathrm{x})\), then \(\frac{\alpha(x)-\beta(x)}{\alpha(x)+\beta(x)}=\)AP EAMCET 2023 Hard
- The values of \(\lambda\) and \(\mu\) for which the system of equations \(x+y+z=6, x+2 y+3 z=10, x+2 y+\lambda z=\mu\) has infinitely many solutions areAP EAMCET 2017 Medium