Find the best tutors and institutes for Class 12 Tuition
Q1:
If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = 2at^2, y = at^4$
If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = 2at^2, y = at^4$
Solution :
Step 1: Identifying the Parametric System
We are given two equations where $x$ and $y$ are functions of a common parameter $t$:
- $x = 2at^2$
- $y = at^4$
Step 2: Differentiating $x$ with respect to $t$
Applying the Power Rule of differentiation ($\frac{d}{dt}[t^n] = nt^{n-1}$):
$\frac{dx}{dt} = \frac{d}{dt}(2at^2)$
$\frac{dx}{dt} = 2a \cdot \frac{d}{dt}(t^2)$
$\frac{dx}{dt} = 2a \cdot (2t)$
$\frac{dx}{dt} = 4at$
Step 3: Differentiating $y$ with respect to $t$
Applying the Power Rule of differentiation:
$\frac{dy}{dt} = \frac{d}{dt}(at^4)$
$\frac{dy}{dt} = a \cdot \frac{d}{dt}(t^4)$
$\frac{dy}{dt} = a \cdot (4t^3)$
$\frac{dy}{dt} = 4at^3$
Step 4: Calculating $\frac{dy}{dx}$
Using the relation $\frac{dy}{dx} = \frac{dy/dt}{dx/dt}$:
$\frac{dy}{dx} = \frac{4at^3}{4at}$
Canceling the common terms $4a$ (assuming $a \neq 0$):
$\frac{dy}{dx} = \frac{t^3}{t}$
Applying the Quotient Rule for exponents ($\frac{t^m}{t^n} = t^{m-n}$):
$\frac{dy}{dx} = t^{3-1}$
$\frac{dy}{dx} = t^2$
Final Solution: $\frac{dy}{dx} = t^2$
More Questions from Class 12 Mathematics Continuity and Differentiability EXERCISE 5.6
- Q2: If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = a \cos \theta, y = b \cos \theta$
- Q3: If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = \sin t, y = \cos 2t$
- Q4: If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = 4t, y = \frac{4}{t}$
- Q5: If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = \cos \theta - \cos 2\theta, y = \sin \theta - \sin 2\theta$
- Q6: If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = a(\theta - \sin \theta), y = a(1 + \cos \theta)$
- Q7: If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = \frac{\sin^3 t}{\sqrt{\cos 2t}}, y = \frac{\cos^3 t}{\sqrt{\cos 2t}}$
- Q8: If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = a\left(\cos t + \log \tan\left(\frac{t}{2}\right)\right), y = a \sin t$
- Q9: If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = a \sec \theta, y = b \tan \theta$
- Q10: If $x$ and $y$ are connected parametrically by the equations, without eliminating the parameter, Find $\frac{dy}{dx}$. $x = a(\cos \theta + \theta \sin \theta), y = a(\sin \theta - \theta \cos \theta)$
- Q11: If $x = \sqrt{a^{\sin^{-1} t}}, y = \sqrt{a^{\cos^{-1} t}}$, show that $\frac{dy}{dx} = -\frac{y}{x}$
CBSE Solutions for Class 12 Mathematics Continuity and Differentiability
- Continuity and Differentiability Class 12 EXERCISE 5.1
- Continuity and Differentiability Class 12 EXERCISE 5.2
- Continuity and Differentiability Class 12 EXERCISE 5.3
- Continuity and Differentiability Class 12 EXERCISE 5.4
- Continuity and Differentiability Class 12 EXERCISE 5.5
- Continuity and Differentiability Class 12 EXERCISE 5.7
Chapters in CBSE - Class 12 Mathematics
Top Tutors who teach Continuity and Differentiability
Top Tutor
Kadiramangalam, Tiruvidamarudur
2 yrs of
Exp
3 students
180 hrs of classes completed
550
per hour
Online Classes
Working in an ICSE school and also Qualified Physics tutor (CTET, TNTET, PG TRB) teaching CBSE & ICSE students with clear explanations, interactive methods, and focused support to improve concepts, confidence, and results. I have helped nearly 30 plus students to overcome the fear of subjects especially physics.
The way of teaching is nice and clear explanation of teaching in theoretical and also practical is clear to understand.
Super Tutor
Banjara Hills, Hyderabad
12 yrs of
Exp
37 students
1639 hrs of classes completed
800
per hour
Online Classes
Tutor's home
Although I haven't taught in schools or colleges, I have been invited to deliver guest lectures at reputed universities. These sessions allowed me to share my expertise with advanced learners and contribute to academic discussions. My focus has always been on delivering value through practical insights, making complex topics accessible and engaging for university students.
The experience is very good , give an detailed explanation with real life examples and also makes the concept easy to understand.
Top Tutor
Yamare Village, Bangalore
8 yrs of
Exp
1 student
8 hrs of classes completed
1500
per hour
Student's Home
Tutor's home
Hello! I’m Anwar, a certified mathematics tutor with over 10 years of experience helping students excel at every stage, from Primary, Middle School to High School and University level. My passion is to make math clear, engaging, and enjoyable for learners worldwide. I specialize in teaching Maths to students from Grade 8 to Grade 12 across multiple curricula including IGCSE/Cambridge, IB (MYP), GCSE, CBSE and ICSE. I focus on concept clarity and exam-oriented preparation, helping students understand not just how to solve questions, but how to approach them logically. My teaching approach is highly interactive and student-centric. Each session begins with clear explanation of concepts, followed by strategies to decode questions and step-by-step solving methods. Students actively participate during the class and solve questions along with me, which allows me to check their understanding in real time. Once the concepts are tested, students solve questions independently while I closely monitor their working and provide instant feedback wherever required. This method helps students strengthen accuracy, speed and confidence, and is especially effective for students who feel weak or anxious in Maths and Science. I offer one-to-one personalized tutoring with a minimum class duration of one hour, ensuring complete attention and customized learning for every student.
Top Tutor
Kushaiguda, Hyderabad
13 yrs of
Exp
1 student
126 hrs of classes completed
450
per hour
Online Classes
Student's Home
Tutor's home
Teaching is my passion I am into teaching profession since 16 years. I like challenges with young minds.. I will make students to confident by explaining concepts, taking special care. Cent percent assurance to child growth, committed to work towards target. I used to counsel the students to succeed in their exams.
Good Teaching, With excellent Communication skills & I'm enjoying, I like to attending classes and also I'm understanding.
Top Tutor
Edapally, Kochi
4 yrs of
Exp
48 hrs of classes completed
500
per hour
Student's Home
Tutor's home
Qualified french teacher and tutor with a master degree in french from delhi university. Working as a language expert in ernst and young. Qualified. Have 4 years of teaching experience. With c1 certification.
Other Subjects in CBSE - Class 12
Download free CBSE - Class 12 Mathematics Continuity and Differentiability EXERCISE 5.6 worksheets
Download Now
