AP EAMCET · Maths · Parabola
The equations of the parabola whose axis is parallel to the \(X\)-axis and which passes through the points \((-2,1),(1,2)(-1,3)\) is
- A \(18 y^2-12 x-21 y-21=0\)
- B \(5 y^2+2 x-21 y+20=0\)
- C \(15 y^2+12 x-11 y+20=0\)
- D \(25 y^2-2 x-65 y+36=0\)
Answer & Solution
Correct Answer
(B) \(5 y^2+2 x-21 y+20=0\)
Step-by-step Solution
Detailed explanation
Let, general equation of this parabola \[ x=A y^2+B y+C \] It is given that, it passes through the points \((-2,1),(1,2)\) and \((-1,3)\) so, we get On solving Eqs. (i), (ii) and (iii), we get \[ A=\frac{-5}{2}, B=\frac{21}{2} \text { and } C=-10 \] Hence, equation of parabola…
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
- In a \(\triangle A B C, C=90^{\circ}\). Then, \(\frac{a^2-b^2}{a^2+b^2}\) is equal toAP EAMCET 2010 Hard
- Let \(E_1=\frac{x^2}{9}+\frac{y^2}{4}=1\) and \(E_2=\frac{x^2}{d^2}+\frac{y^2}{b^2}=1\) be two ellipses and \(\mathrm{R}\) be a rectangle with sides parallel to the coordinate axes. Let \(E_1\) be inscribed ellipse in \(\mathrm{R}\) and \(E_2\) be circumscribed ellipse on R. If \(E_2\) passes through \((0,4)\) thenAP EAMCET 2022 Medium
- If \(\bar{a}=\bar{i}-2 \bar{j}-3 \bar{k}, \bar{b}=-2 \bar{i}+3 \bar{j}+4 \bar{k}, \bar{c}=5 \bar{i}-4 \bar{j}+3 \bar{k}\) and \(\bar{d}=3 \bar{i}+\bar{j}+5 \bar{k}\) are four vectors then \((\bar{a} \times \bar{b}) \times(\bar{c} \times \bar{d})=\)AP EAMCET 2025 Medium
- The remainder obtained when \(5^{99}\) is divided by 13 isAP EAMCET 2017 Medium
- Let \(A=\left(\begin{array}{ll}-\cot \theta & \operatorname{cosec} \theta \\ \operatorname{cosec} \theta & -\cot \theta\end{array}\right)\). If \(A^{-1}=A\) at \(\theta=\theta_1\) and \(A^{-1}\) \(+\mathrm{A}=\mathrm{O}\) at \(\theta=\theta_2\), then which one of the following is True?AP EAMCET 2023 Medium
- The angle between the tangents drawn at \((0,0)\) to the curves \(y^3-x^2 y+5 y-2 x=0\) and \(x^4-x^3 y^2+5 x+2 y=0\) isAP EAMCET 2022 Medium
More PYQs from AP EAMCET
- If two angles of \(\triangle A B C\) are \(45^{\circ}\) and \(60^{\circ}\), then the ratio of the smallest and the greatest sides areAP EAMCET 2007 Medium
- The magnetic field due to current carrying circular loop of radius \(6 \mathrm{~cm}\) at a point on the axis at a distance of \(8 \mathrm{~cm}\) from centre is \(27 \mu \mathrm{T}\). The magnetic field at the centre of the current carrying loop is.AP EAMCET 2022 Medium
- Which of the following statements are not correct?
i. Atomic radius of \(\mathrm{Ga}\) is less than that of \(\mathrm{Al}\)
ii. The order of ionization enthalpy of group 13 elements is \(\mathrm{B}>\mathrm{Al}>\mathrm{Ga}>\mathrm{In}>\mathrm{Tl}\)
iii. Boron trioxide is amphoteric in natureAP EAMCET 2023 Easy - A person walks along a straight road from his house to a market \(2.5 \mathrm{~km}\) away with a speed of \(5 \mathrm{~km} / \mathrm{h}\) and instantly turns back and reaches his house with a speed of \(7.5 \mathrm{~km} / \mathrm{h}\). The average speed of the person during the time interval 0 to \(50 \mathrm{~min}\) is \((\mathrm{in} \mathrm{m} / \mathrm{s})\)AP EAMCET 2014 Easy
- \(\lim _{x \rightarrow 0}(1+3 x)^{\frac{2}{x}}=\)AP EAMCET 2020 Medium
- If \(y=\operatorname{Tan}^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right)\) for \(0 < |x| < 1\), then \(\frac{d y}{d x}=\)AP EAMCET 2017 Medium