AP EAMCET · Maths · Application of Derivatives
If a normal drawn at a point \(P\) to the curve \(y=\sin x\) passes through the origin, then the locus of \(\mathrm{P}\) is
- A \(\mathrm{x}^2=\mathrm{y}^2-\mathrm{y}^4\)
- B \(x+y=1\)
- C \(\frac{1}{y^2}-\frac{1}{x^2}=1\)
- D \(\frac{1}{y^4}-\frac{1}{x^4}=1\)
Answer & Solution
Correct Answer
(A) \(\mathrm{x}^2=\mathrm{y}^2-\mathrm{y}^4\)
Step-by-step Solution
Detailed explanation
\(y=\sin x \Rightarrow \frac{d y}{d x}=\cos x\) Slope of normal \(\Rightarrow m=-\frac{1}{\frac{d y}{d x}}=-\frac{1}{\cos x}\) Let the co-ordinate of point \(\mathrm{P}\) is \((h, k)\) Then, \(m=-\frac{1}{\cos h}\) Equation of normal, which passes through \((0,0)\) 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
- In \(\triangle \mathrm{ABC}\), if \(\cos \mathrm{A} \cdot \cos \mathrm{B} \cdot \cos \mathrm{C}=\frac{1}{5}\), then \(\tan \mathrm{A} \tan \mathrm{B}+\) \(\tan \mathrm{B} \tan \mathrm{C}+\tan \mathrm{C} \tan \mathrm{A}=\)AP EAMCET 2023 Medium
- Which of the following is differentiable at \(x=0 ?\)AP EAMCET 2022 Easy
- If \(y=t^2+t^3\) and \(x=t-t^4\) then \(\frac{d^2 y}{d x^2}\) at \(t=1\) isAP EAMCET 2024 Hard
- If \(k \in N\) then \(\lim _{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots+\frac{1}{k n}\right]=\)AP EAMCET 2025 Medium
- \(P\) is a variable point such that the distance of \(P\) from \(A(4,0)\) is twice the distance of \(P\) from \(B(-4,0)\). If the line \(3 y-3 x-20=0\) intersects the locus of P at the points C and D , then the distance between C and D isAP EAMCET 2024 Easy
- The period of \(\sin ^4 x+\cos ^4 x\) isAP EAMCET 2009 Easy
More PYQs from AP EAMCET
- The of lime water isAP EAMCET 2022 Medium
- In a time of 2 s , the amplitude of a damped oscillator becomes \(\frac{1}{e}\) times its initial amplitude A. In the next two seconds, the amplitude of the oscillator isAP EAMCET 2024 Hard
- If a set of 30 games cards, 17 are white and rest are green. Out of 30,4 white and 5 green are marked IMPORTANT. If a card is chosen randomly from this set, then possibility of choosing a green card or an 'IMPORTANT' card isAP EAMCET 2022 Easy
- If a complex number \(z\) satisfies
\(|z|^2+1=\mid z^2-1\), then the locus of \(z\) isAP EAMCET 2018 Easy - If the function \(y=g(x)\) representing the slopes of the tangents drawn to the curve \(y=3 x^4-5 x^3-12 x^2+18 x+3\) is strictly increasing then the domain of \(g(x)\) isAP EAMCET 2025 Medium
- Statement-I : In the interval \([0,2 \pi]\), the number of common solutions of the equations \(2 \sin ^2 \theta-\cos 2 \theta=0\) and \(2 \cos ^2 \theta-3 \sin \theta=0\) is two.
Statement-II : The number of solutions of \(2 \cos ^2 \theta-3 \sin \theta=0\) in \([0, \pi]\) is two.AP EAMCET 2025 Medium