Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A circle touches the y-axis at the point  and passes through the point <img alt="(2,0)." src="https://l

A circle touches the y-axis at the point (0,4) and passes through the point (2,0). Which of the following lines is not tangent to this circle ?

Option: 1

4x-3y+17=0
 


Option: 2

3x+4y-6=0


Option: 3

4x+3y-8=0

 


Option: 4

3x-4y-24=0


Answers (1)

best_answer

 

 

Circle(Definition) -

Circle

Equation of circle

Central Form:

The equation of a circle with centre at C (h,k) and radius r is (x-h)2+(y-k)2=r2.

 

Let P(x, y) be any point on the circle. Then, by definition, | CP | = r.

Using the distance formula, we have

\\ \mathrm{{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\sqrt{(x-h)^{2}+(y-k)^{2}}=r}} \\\\ \mathrm{i.e.\;\;\;\;\;\;\;\;\;\;\;\;\;\;{(x-h)^{2}+(y-k)^{2}=r^{2}}}

If the centre of the circle is the origin or (0,0) then equation of the circle becomes
\\(x-0)^{2}+(y-0)^{2}=r^{2}\\\text{i.e. }x^2+y^2=r^2

General Form:

The equation of a circle with centre at (h,k) and radius r is 

\\ {\Rightarrow(x-h)^{2}+(y-k)^{2}=r^{2}} \\ {\Rightarrow x^{2}+y^{2}-2 h x-2 k y+h^{2}+k^{2}-r^{2}=0\;\;\;\;\;\;\;\;\;\;\;\ldots(i)} \\ {\text { Which is of the form : }} \\ {\mathbf{x}^{2}+\mathbf{y}^{2}+2 \mathbf{g} \mathbf{x}+2 \mathbf{f} \mathbf{y}+\mathbf{c}=\mathbf{0}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ldots(ii)}

-

 

 

Family of Circles -

 

  1. Equation of the family of circles passing through the point of intersection of a given circle S = 0 and a line L = 0is S + λL  where, λ is a parameter.


 

-

 

 

 

 

 

Equation of family of circle touches at (0,4) (x-0)^{2}+(y-4)^{2}+\lambda x=0

This family of circle passes through (2,0) 

4+16+2 \lambda=0 \Rightarrow \lambda=-10

x^{2}+y^{2}-10 x-8 y+16=0

Center (5, 4) and radius = 5

Now check the option 

4x+3y-8=0

\left|\frac{4 \times 5+3 \times 4-8}{5}\right|=\frac{24}{5} \neq 5

Posted by

avinash.dongre

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025 paper 2 final answer key out; NTA drops 4 questions, 2 from BPlanning
anam-khan

JEE Main 2025 session 2 answer key out for BArch, BPlanning; response sheet on jeemain.nta.nic.in
anam-khan

JEE Mains 2025 Paper 2 Answer Key LIVE: BArch final answer key PDF expected soon at jeemain.nta.nic.in

Latest Question