TS EAMCET · Maths · Parabola
The equation of the common tangent of the parabolas \(x^2=108 y\) and \(y^2=32 x\) is
- A \(2 x+3 y+36=0\)
- B \(2 x+3 y=36\)
- C \(3 x+2 y+36=0\)
- D \(3 x+2 y=36\)
Answer & Solution
Correct Answer
(A) \(2 x+3 y+36=0\)
Step-by-step Solution
Detailed explanation
(a) Given equation of parabola \(x^2=108 y(4 a=108 \Rightarrow a=27)\) Equation of tangent, \(y=m x-27 m^2\) \(\ldots(\mathrm{i})\) And equation of parabola \(y^2=32 x(4 a=32 \Rightarrow a=8)\) Equation of tangent, \(y=m x+\frac{8}{m}\) \(\ldots(\mathrm{ii})\) Since Eqs. (i) and…
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 thenTS EAMCET 2021 Easy
- A class has fifteen boys and five girls. Suppose three students are selected at random from the class. The probability that there are two boys and one girl isTS EAMCET 2011 Medium
- If \(\sinh x=\frac{3}{4}\) and \(\cosh y=\frac{5}{3}\), then \(x+y=\)TS EAMCET 2018 Medium
- Let the line \(x-y+1=0\) intersect the circle \(x^2+y^2+2 x\) \(+2 y+1=0\) in two points \(A\) and \(B\). If \(A B\) is the diameter of the circle \(x^2+y^2+2 g x+2 f y+c=0\) then \(g+f=\)TS EAMCET 2023 Easy
- The angle of elevation of a stationary cloud from a point \(2500 \mathrm{~m}\) above a lake is \(15^{\circ}\) and from the same point the angle of depression of its reflection in the lake is \(45^{\circ}\). The height (in metres) of the cloud above the lake, given that \(\cot 15^{\circ}=2+\sqrt{3}\), isTS EAMCET 2011 Hard
- The slope of a common tangent to the ellipse \(\frac{x^2}{49}+\frac{y^2}{4}=1\) and the circle \(x^2+y^2=16\) isTS EAMCET 2018 Easy
More PYQs from TS EAMCET
- Identify the reactions in which \(\mathrm{H}_2\) is liberated? (i) \(\mathrm{Zn}+\mathrm{NaOH}(a q) \longrightarrow\) (ii) \(\mathrm{HCOOH} \xrightarrow[\text { Conc. } \mathrm{H}_2 \mathrm{SO}_4]{373 \mathrm{~K}}\) (iii) \(\mathrm{CH}_4(g)+\mathrm{H}_2 \mathrm{O}(g) \xrightarrow[\mathrm{Ni}]{\stackrel{1270 \mathrm{~K}}{\longrightarrow}}\) (iv) \(\mathrm{Zn}+\mathrm{H}^{+}(a q) \longrightarrow\) (v) \(\mathrm{C}(s)+\mathrm{H}_2 \mathrm{O}(g) \xrightarrow{1270 \mathrm{~K}}\)TS EAMCET 2018 Medium
- A wire of cross-sectional area \(10^{-6} \mathrm{~m}^2\) is elongated by \(0.1 \%\) when the tension in it is 1000 N . The Young's modulus of the material of the wire is (Assume radius of the wire is constant)TS EAMCET 2024 Easy
- and are two points on the ellipse with eccentricity . If is a focal chord and , then and areTS EAMCET 2022 Hard
- The angle between the lines whose direction ratios satisfy the equations \(l+m+n=0\) and \(l^2=m^2+n^2\) isTS EAMCET 2020 Medium
- \(F_{\mathrm{pp}}, F_{\mathrm{nn}}\) and \(F_{\mathrm{np}}\) are the nuclear forces between proton-proton, neutron-neutron and neutron-proton respectively. Then relation between them isTS EAMCET 2008 Easy
- In a bcc lattice having the edge length of \(200 \mathrm{pm}\), the cation has the radius of \(70 \mathrm{pm}\). The radius ratio of \(\frac{r^{+}}{r^{-}}\)is (Given, \(\sqrt{2}=1.4, \sqrt{3}=1.7\) and \(\sqrt{6}=2.4\) )TS EAMCET 2020 Easy