TS EAMCET · Maths · Parabola
From a point \((C, 0)\) three normals are drawn to the parabola \(y^2=x\). Then,
- A \(C < \frac{1}{2}\)
- B \(C=\frac{1}{2}\)
- C \(C>\frac{1}{2}\)
- D \(\frac{1}{2}>C>\frac{1}{4}\)
Answer & Solution
Correct Answer
(C) \(C>\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Given, \(y^2=x\) \[ \therefore \quad 4 a=1 \Rightarrow a=\frac{1}{4} \] Any normal to the parabola is \[ y=m x-2 a m-a m^3 \] If it passes through \((C, 0)\), then If it passes through \((C, 0)\), then…
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 area of the region bounded by \(y=|x|\) and \(y=1-|x|\) isTS EAMCET 2018 Easy
- In \(\triangle A B C, \angle B=90^{\circ}\) and \((b+a)\) is always a constant. In order that \(\triangle A B C\) encloses the maximum area, \(\angle C=\)TS EAMCET 2020 Hard
- Let \(\frac{1}{\left(x^2-3\right)^2}=\frac{A_1}{x-\sqrt{3}}+\frac{A_2}{(x-\sqrt{3})^2}\) \(+\frac{A_3}{x+\sqrt{3}}+\frac{A_4}{(x+\sqrt{3})^2}\). Then, consider the following statements (i) All the \(A_{\mathrm{i}}\) 's are not distinct (ii) There exists a pair, \(A_p\) and \(A_q\) such that \(A_p^2=A_q^2(p \neq q)\) (iii) \(\sum_{i=1}^4 A_i=\frac{1}{6}\) (iv) \(\sum_{i=1}^4 A_i=1\) Which one of the following is true?TS EAMCET 2019 Medium
- If the augmented matrix corresponding to the system of equations \(x+y-z=1\), \(2 x+4 y-z=0\) and \(3 x+4 y+5 z=18\) is transformed to \(\left[\begin{array}{cccc}1 & a & 0 & -1 \\ 0 & 2 & 1 & b \\ 0 & 0 & c & 32\end{array}\right]\), then \(\sqrt{a+b+c}=\)TS EAMCET 2025 Medium
- If , thenTS EAMCET 2021 Easy
- The points in the Argand plane given by form aTS EAMCET 2018 Easy
More PYQs from TS EAMCET
- A rod of length units slides with its ends on the coordinate axes. The locus of the midpoint of the rod isTS EAMCET 2021 Easy
- If the line divides the line segment joining the points and in the ratio , then the point which divides in the ratio isTS EAMCET 2022 Easy
-
If \(A(2,-3)\) and \(B(-2,1)\) are two vertices of a triangle and third vertex moves on the line \(2 x+3 y=9\), then the locus of the centroid of the triangle isTS EAMCET 2023 Easy - Total emf produced in a thermocouple does not depend onTS EAMCET 2012 Easy
- \(\cot \theta-\tan \theta-2 \tan 2 \theta-4 \tan 4 \theta=\)TS EAMCET 2018 Medium
- Let \(x\) denote the number of ways of selecting at least one ball from a bag containing 3 identical red balls, 4 identical blue balls and 5 identical green balls. Let \(y\) denote the number of ways in which a student will fail in an examination, when he has to write the examination in 5 different subjects. Then \(x+y=\)TS EAMCET 2020 Medium