TS EAMCET · Maths · Parabola
For the parabola \(y^2+6 y-2 x=-5\) I. the vertex is \((-2,-3)\) II. the directrix is \(y+3=0\) Which of the following is correct?
- A Both I and II are correct
- B I is true, II is false
- C Both I and II are false
- D I is false, II is true
Answer & Solution
Correct Answer
(B) I is true, II is false
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} \Rightarrow & & y^2+6 y-2 x & =-5 \\ \Rightarrow & & y^2+6 y & =2 x-5 \\ \Rightarrow & & y^2+6 y+9 & =2 x-5+9 \\ \Rightarrow & & (y+3)^2 & =2 x+4 \\ \Rightarrow & & (y+3)^2 & =2(x+2) \end{aligned} \]…
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
- If \(x=\frac{\mathrm{t}^2}{1+\mathrm{t}^5}, y=\frac{2 \mathrm{t}^3}{1+\mathrm{t}^5}\) and \(\mathrm{t} \neq-1\) is a parameter then \(\frac{d y}{d x}=\)TS EAMCET 2025 Medium
- The area bounded by \(y=x^2+2, x\)-axis, \(x=1\) and \(x=2\) isTS EAMCET 2004 Medium
- \(\int \frac{2 x+2}{\sqrt{x^2-4 x-5}} d x\) is equal toTS EAMCET 2016 Medium
- For \(h, k \in N\), let \(\mathrm{P}(h, k)\) be the point of intersection of the curves \(x^2 y-x^3=8\) and \(y^3-x y^2=32\). If \(\theta\) is the acute angle between these two curves at \(P, \operatorname{then} \tan \theta=\)TS EAMCET 2023 Easy
- All possible 5 digit numbers each having 5 distinct digits are formed using digits \(1,2,3,5,6,8\). Among them, the number of numbers which are divisible by 3 but not by 6 isTS EAMCET 2023 Easy
- \[ \begin{aligned} & \left.\sin ^2 \beta^{\circ}\right)+\sin ^2\left(6^{\circ}\right)+\sin ^2\left(9^{\circ}\right)+\ldots+\sin ^2\left(84^{\circ}\right) \ & +\sin ^2\left(87^{\circ}\right)+\sin ^2\left(90^{\circ}\right)= \end{aligned} \]TS EAMCET 2019 Easy
More PYQs from TS EAMCET
- If \((2 x-y+1)+i(x-2 y-1)=2-3 i\), then the multiplicative inverse of \((x-i y)\) isTS EAMCET 2022 Medium
- Where should an object be placed on the axis of a convex lens of focal length so as to achieve magnification of ? (Distances are measured from optic centre of the lens)TS EAMCET 2018 Easy
- If \(A+C=2 B\), then \(\frac{\cos C-\cos A}{\sin A-\sin C}\) is equal toTS EAMCET 2005 Easy
- Match the following:
The correct answer is \(\begin{array}{lll} \text { A } & \text { B } & \text { C } \end{array} \)TS EAMCET 2022 Medium - Three moles of an ideal gas undergoes a cyclic process ABCA as shown in the figure. The pressure, volume and absolute temperature at points \(\mathrm{A}, \mathrm{B}\) and C are respectively \(\left(\mathrm{P}_1, \mathrm{~V}_1\right.\), \(\left.T_1\right),\left(P_2, 3 V_1, T_1\right)\) and \(\left(P_2, V_1, T_2\right)\). Then the total work done in the cycle ABCA is (R- Universal gas constant).
TS EAMCET 2025 Medium - If the line joining the points \(A(b \cos \alpha, b \sin \alpha)\) and \(B(a \cos \beta, a \sin \beta)\) is extended to the point \(N(x, y)\) such that \(A N: N B=b: a\), thenTS EAMCET 2018 Hard