AP EAMCET · Maths · Parabola
The angle between the tangents drawn from the point \((1,4)\) to the parabola \(y^2=4 x\) is
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\(y^2=4x \Rightarrow a=1\) \(y=mx+\frac{a}{m} \Rightarrow 4 = m(1) + \frac{1}{m}\) \(m^2 - 4m + 1 = 0\) \(m_1+m_2 = 4, m_1m_2 = 1\) \(\tan\theta = \left| \frac{m_1-m_2}{1+m_1m_2} \right| = \left| \frac{\sqrt{(m_1+m_2)^2 - 4m_1m_2}}{1+m_1m_2} \right|\)…
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
- Let \(\mathrm{PQR}\) be a right angled isosceles triangle, right angled at \(P(2,1)\). If the equation of the side \(Q R\) is \(2 x+y=3\), then the equation of one of the sides other than \(Q R\) isAP EAMCET 2023 Easy
- The probability distribution of a random variable \(X\) is given below.
Then the variance of \(X\) isAP EAMCET 2011 Easy - Let \(x+y=k\) be a normal to the parabola \(y^2=12 x\). If \(p\) is length of the perpendicular from the focus of the parabola onto this normal, then \(4 k-2 p^2\) is equal toAP EAMCET 2012 Medium
- If two numbers \(x\) and \(y\) are chosen one after the other at random with replacement from the set of number \(\{1,2,3\) ..., 10\(\}\), then the probability that \(\left|x^2-y^2\right|\) is divisible by 6 isAP EAMCET 2024 Medium
- If the system of simultaneous linear equations \(\mathrm{x}+\mathrm{y}+\mathrm{z}=\lambda, 5 \mathrm{x}-\mathrm{y}+\mu \mathrm{z}=10\) and \(2 \mathrm{x}+3 \mathrm{y}-\mathrm{z}=6\) has unique solution, thenAP EAMCET 2022 Easy
- If and are two functions defined by and , thenAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- The vector equation of the plane passing through the points and isAP EAMCET 2019 Easy
- A silver wire of length \(3 \mathrm{~m}\) and of cross-sectional area \(6.14 \times 10^{-6} \mathrm{~m}^2\) carries a current of 6 A. Atomic weight and density of silver are 108 and \(10500 \mathrm{kgm}^{-3}\), respectively. A silver atom contributes one free electron for conduction. Avogadro number is \(6.023 \times 10^{23} / \mathrm{mol}\). Drift velocity of electrons in silver is, close toAP EAMCET 2021 Medium
- A circle is drawn touching the \(X\)-axis, with its centre at the point of reflection of \((m, n)\) on the line \(y-x=0\). Then the equation of the circle isAP EAMCET 2020 Medium
- Two points and with co-ordinates and are given respectively. Then, the locus of a point so that the area of is 9 sq.units is given by _____AP EAMCET 2020 Medium
- The force acting per unit length when a very long straight conductor is carrying a steady current of \(1 \mathrm{~A}\) and the direction of the current is from south to north is
(The horizontal component of the earth's magnetic field at the place is \(3 \times 10^{-5} \mathrm{~T}\) and the direction of the field is from the geographical south to geographical north.)AP EAMCET 2023 Easy - The correct statement regarding X and Y in the following set of reactions is
AP EAMCET 2025 Medium