AP EAMCET · Maths · Parabola
If the line \(y=2 x+k\) is normal to the parabola \(y^2=4 x\), then \(k=\)
- A -10
- B 10
- C 12
- D –12
Answer & Solution
Correct Answer
(D) –12
Step-by-step Solution
Detailed explanation
Since, equation of normal to the parabola \(y^2=4 a x\) having slope \(m\) is \(y=m x-2 a m-a m^3\). So, equation of normal to the parabola \(y^2=4 x\) is \[ y=2 x+k \] Therefore, \[ \begin{aligned} k & =-2(1)(2)-(1)(2)^3 \\ & =-4-8=-12 \end{aligned} \] Hence, option (4) is…
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
- Find the remainder when \(x^4-11 x^3+44 x^2-76 x+48\) is divided by \(x^2-7 x+12\).AP EAMCET 2020 Medium
- If \(2 x^2+3 x y-2 y^2-5 x+2\) fy \(-3=0\) represents a pair of straight lines, then one of the possible values of \(f\) isAP EAMCET 2025 Medium
- A point on the straight line \(3 x+5 y=15\) which is equidistant from the coordinate axes will lie inAP EAMCET 2023 Medium
- If \(\left(\mathrm{l}_1, \mathrm{~m}_1, \mathrm{n}_1\right),\left(\mathrm{l}_2, \mathrm{~m}_2, \mathrm{n}_2\right)\) are the direction cosines of two lines, then \(\left(1_1 m_2-1_2 m_1\right)^2+\left(m_1 n_2-m_2 n_1\right)^2+\) \(\left(\mathrm{n}_1 \mathrm{l}_2-\mathrm{n}_2 \mathrm{l}_1\right)^2+\left(\mathrm{l}_1 \mathrm{l}_2+\mathrm{m}_1 \mathrm{~m}_2+\mathrm{n}_1 \mathrm{n}_2\right)^2=\)AP EAMCET 2023 Hard
- If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are three unit vectors such that \(\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=\frac{\sqrt{3}}{2} \mathbf{b}+\frac{1}{2} \mathbf{c}\), then the angles between \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{a}, \mathbf{c}\) respectively areAP EAMCET 2019 Easy
- The points and areAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- The general solution of the differential equation \(\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x\) isAP EAMCET 2024 Medium
- What is the shape of \(\mathrm{I}_3^{-}\)ion?AP EAMCET 2020 Easy
- Fusion reaction is initiated with the help ofAP EAMCET 2021 Easy
- A lens forms real and virtual images of an object when the object is at and distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (Take the magnification of the real image as )AP EAMCET 2018 Hard
- In an optical fibre, core and cladding were made with materials of refractive indices 1.5 and 1.414 respectively. To observe total internal reflection, what will be the range of incident angle with the axis of optical fibre?AP EAMCET 2010 Medium
- If the sum of the coefficients of even powers of \(x\) in the expansion of \(\left(1-x+x^2\right)^{2 n}\) is 3281 , then \(\mathrm{n}=\)AP EAMCET 2023 Medium