Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain Solution R.D.Sharma Class 12 Chapter 15 Tangents and Normals Exercise 15.1 Question 15 maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 15 Tangents and Normals Exercise 15.1 Question 15 maths Textbook Solution.

Answers (1)

Answer: The requried point are (0,0) \&(2 a,-2 a)

Hint:\text { The slope of the tangent is the limit of } \frac{\Delta y}{\Delta x} \text { as } \Delta x \text { approaches zero. }

Given:The Curve is 2 a^{2} y=x^{3}-3 a x^{2} \rightarrow(1)

Solution:2 a^{2} y=x^{3}-3 a x^{2}

\text { Differentiating the above with respect to } x

\therefore \frac{d}{d x}\left(\mathrm{x}^{n}\right)=n x^{n-1}, \frac{d}{d x}(\text { constant })=0

2 a^{2} \frac{d y}{d x}=3 x^{3-1}-3 a(2)(x)^{2-1}

2 a^{2} \frac{d y}{d x}=3 x^{2}-6 a x

\frac{d y}{d x}=\frac{1}{2 a^{2}}\left[3 x^{2}-6 a x\right]

\text { Slope } \mathrm{m}_{1}=\frac{d y}{d x}=\frac{1}{2 a^{2}}\left[3 x^{2}-6 a x\right] \rightarrow(2)

Also

\text { Slope } \mathrm{m}_{2}=\frac{d y}{d x}=\tan \theta

\tan 0^{\circ}=0

\text { [slope is parallel to } x \text { -axis] }

m_{1}=m_{2}

\frac{1}{2 a^{2}}\left[3 x^{2}-6 a x\right]=0

3 x^{2}-6 a x=0

\begin{aligned} &3 x(x-2 a)=0 \\ &3 x=0 \text { or } x-2 a=0 \\ &x=0 \text { or } x=2 a \end{aligned}

\text { When put } x=0 \text { in eqn(1) } 2 a^{2} y=x^{3}-3 a x^{2}

\begin{aligned} &2 a^{2} y=(0)^{3}-3 a(0)^{2} \\ &2 a^{2} y=0 \\ &y=0 \end{aligned}

\text { When put } x=2 a \text { in eqn (1) } 2 a^{2} y=x^{3}-3 a x^{2}

\begin{aligned} &2 a^{2} y=(2 a)^{3}-3 a(2 a)^{2} \\ &2 a^{2} y=8 a^{3}-3 a\left(4 a^{2}\right) \\ &2 a^{2} y=8 a^{3}-12 a^{3} \\ &2 a^{2} y=-4 a^{3} \\ &y=-2 a \end{aligned}

Thus the requried points are (0,0) \&(2 a,-2 a)

Posted by

infoexpert21

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE announces deadline for Class 10, 12 direct admissions, subject change
anam-khan

CBSE warns about unauthorised sources offering ‘quick’ ways of getting duplicate marksheets, certificates
anam-khan

CBSE unveils 8 major changes for Class 10, 12 board exams; what students need to know

Latest Question