TS EAMCET · Maths · Parabola
Let \(P\) represent the point \((3,6)\) on the parabola \(y^2=12 x\). For the parabola \(y^2=12 x\), if \(l_1\) is the length of the normal chord drawn at \(P\) and \(l_2\) is the length of the focal chord drawn through \(P\), then \(\frac{l_1}{l_2}=\)
- A \(2 \sqrt{2}\)
- B 3
- C \(4 \sqrt{2}\)
- D 5
Answer & Solution
Correct Answer
(A) \(2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
We know that, length of normal of parabola \(y^2=4 a x\) at \(\left(a t^2, 2 a t\right)=8 a \sqrt{t^2+1}\) and length of focal chord \(=a\left(t+\frac{1}{t}\right)^2\). Point \(P(3,6)\) lie on parabola \(y^2=12 x\) \(\therefore\) Here \(a=3, t=1\) Hence…
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 \(f(x)=\left\{\begin{array}{cc}\sin x & \text { if } x \leq 0 \ x^2+a^2 & \text { if } 0 < x < 1 \ b x+2 & \text { if } 1 \leq x \leq 2 \ 0 & \text { if } x>2\end{array}\right.\) is continuous on \(\mathrm{IR}\), then \(a+b+a b=\)TS EAMCET 2017 Easy
- If \((1,-2)\) is the focus and \(x+y-2=0\) is the directrix of the ellipse \(17 x^2-2 x y+17 x^2-32 x+76 x+86-0\), then its eccentricity isTS EAMCET 2019 Hard
- In \(\triangle A B C,(a+b+c)\left(\tan \frac{A}{2}+\tan \frac{B}{2}\right)\) is equal toTS EAMCET 2007 Medium
- If \(\frac{3 x+2}{(x+1)\left(2 x^2+3\right)}=\frac{A}{x+1}+\frac{B x+C}{2 x^2+3}\), then \(A-B+C=\)TS EAMCET 2018 Easy
- If is continuous at , thenTS EAMCET 2018 Easy
- An ellipse passing through \((4 \sqrt{2}, 2 \sqrt{6})\) has foci at \((-4,0)\) and \((4,0)\). Then, its eccentricity isTS EAMCET 2014 Medium
More PYQs from TS EAMCET
- Let \(X\) and \(Y\) be two events of a sample space such that \(P(X)=\frac{1}{3}, P(X / Y)=\frac{1}{2}\) and \(P(Y / X)=\frac{2}{5}\) thenTS EAMCET 2020 Easy
- If an electron has an energy such that its de-Broglie wavelength is \(5500 Å\), then the energy value of that electron is \(\left(h=6.6 \times 10^{-34} \mathrm{Js}, m_{\mathrm{c}}=9.1 \times 10^{-31} \mathrm{~kg}\right)\)TS EAMCET 2015 Easy
- A point mass oscillates along the \(X\)-axis according to the law \(x=x_0 \cos \left(\omega t-\frac{\pi}{4}\right)\). If the acceleration of the particle is written as \(a=A \cos (\omega t-\delta)\), thenTS EAMCET 2020 Easy
- \(\mathrm{AlCl}_3\) in water at \(\mathrm{pH} < 7\) formsTS EAMCET 2018 Medium
- Let \(f: R \rightarrow R\) be a bijection. \(A\) curve represented by \(y=f(x)\) is such that \(f^{\prime}(x)>0 \forall x \in \mathbf{R}\). The tangent and normal drawn at \(P(\alpha, 1)\) on the curve cuts the \(X\)-axis at \(A, B\) respectively and \(C\) is the foot of the perpendicular from \(P\) onto the \(X\)-axis. If \(P(\alpha, \mathrm{l})\) is such a point that \(A C+C B\) is minimum, then the tangent at \(P\) is parallel to the lineTS EAMCET 2020 Hard
- A radioactive source has a half-life of \(6 \mathrm{~h}\). A freshly prepared sample of the same exhibits radioactivity 32 times the permissible safe value. The minimum time after which it would be possible to work safely with the source isTS EAMCET 2020 Easy