Question

if a line 3x-4y=lambda cuts the circle x^2+y^2-4x-8y-5=0 in to two points then limits of lambda are
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Answer 1

Answer:

Step-by-step explanation:

perpendicular distance, d between centre of circle and line should be 0≤d<r centre of circle

=(−g,−f)=(  

2

4

​  

,  

2

8

​  

)

=(2,4) radius,

r=  

f  

2

+g  

2

−c

​  

=  

4+16+5

​  

=5

⇒  

∣

∣

∣

∣

∣

​  

 

5

3(2)−4(4)−λ

​  

 

∥

∥

∥

∥

∥

​  

≤r

⇒∣10+λ∣<5r⇒∣λ+10∣<25

⇒−25<λ+10<25⇒  

−35<λ<15

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