TS EAMCET · Maths · Straight Lines
If \(x^2=8\) ay is the transformed equation of \(x^2-4 y+6 x+\) \(15=0\) when the origin is shifted to the point \((\alpha, \beta)\) by translation of axes, then \(2 \alpha+8 \beta^2=\)
- A 8
- B 18
- C 12
- D 16
Answer & Solution
Correct Answer
(C) 12
Step-by-step Solution
Detailed explanation
Translated equation of \(x^2-8 a y=0\) is with point \((\alpha\), \(\beta\) ) is \[ \begin{aligned} & (x-\alpha)^2-8 a(y-\beta) \equiv x^2-4 y+6 x+15 \text { (Given) } \\ & \Rightarrow x^2-8 a y-2 \alpha x+\alpha^2+8 a \beta \\ & =x^2-4 y+6 x+15 \end{aligned} \] On comparing we…
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 quadratic equation whose roots are \(\sin ^2 18^{\circ}\) and \(\cos ^2 36^{\circ}\) isTS EAMCET 2023 Easy
- Imaginary part of isTS EAMCET 2019 Medium
- If \(f(x)= \begin{cases}\frac{\sin (1+[x])}{[x]}, & \text { for }[x] \neq 0 \ 0, & \text { for }[x]=0\end{cases}\) where \([x]\) denotes the greatest integer not exceeding \(x\), then \(\lim _{x \rightarrow 0^{-}} f(x)\) is equal toTS EAMCET 2007 Medium
- Let \(n=1 !+4 !+7 !+\ldots+400 !\). Then ten's digit of \(n\) isTS EAMCET 2010 Hard
- If \(A=\left[\begin{array}{ll}0 & 5 \\ 0 & 0\end{array}\right]\) and \(f(x)=x+x^2+\ldots+x^{2018}\), then \(f(A)+I=\)TS EAMCET 2019 Easy
- \(\int_{1 / 2}^2\left|\log _{10} x\right| d x=\)TS EAMCET 2023 Hard
More PYQs from TS EAMCET
- Which of the following are correct? (1) Electron density in \(X Y\) plane for \(d_{x^2-y^2}\) orbital is zero. (2) The energy of \(3 p\)-orbital is higher than the energy of \(2 p\)-orbital. (3) \(3 p_z\)-orbital has one angular node. (4) 4 -orbital has no radial node.TS EAMCET 2018 Medium
- The rank of the matrix \(\left[\begin{array}{cccc}3 & 2 & 1 & -4 \\ 2 & 3 & 0 & -1 \\ 1 & -6 & 3 & -8\end{array}\right]\) isTS EAMCET 2018 Easy
- A person observes the top of a tower from a point \(A\) on the ground. The elevation of the tower from this point is \(60^{\circ}\). He moves \(60 \mathrm{~m}\) in the direction perpendicular to the line joining \(A\) and base of the tower. The angle of elevation of the tower from this point is \(45^{\circ}\). Then, the height of the tower (in metres) isTS EAMCET 2013 Medium
- Let \(\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{b}=3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}\) be two vectors. Then the projection vector of \(\mathbf{b}\) on a vector perpendicular to \(\mathbf{a}\) isTS EAMCET 2021 Easy
- If a normal chord of a parabola \(y^2=4 a x\) subtends a right angle at the origin, then the slope of that normal chord isTS EAMCET 2018 Medium
- If \(x+2 y+k=0, k>0\) is a tangent to the ellipse \(2 x^2+y^2=2\), then the equation of the normal to the given ellipse at \(\left(\frac{1}{\sqrt{2}}, \frac{k}{3}\right)\), isTS EAMCET 2020 Medium