Question

find the length of the chord made by 3 x square minus y square equal to 3 and Y + x minus 5 is equal to zero​

Answer 1

Answer:

Step-by-step explanation:

Equation of the given line is x−y+2=0   ...(1)

Equation of the circle is 3x  

2

+3y  

2

−29x−19y+56=0   ...(2)

Solving (1) and (2), we get

3x  

2

+3(x+2)  

2

−29x−19(x+2)+56=0

⇒3x  

2

+3(x  

2

+4x+4)−29x−19x−38+56=0

⇒3x  

2

+3x  

2

+12x+12−29x−19x−38+56=0

⇒6x  

2

−36+30=0⇒(x−5)(x−1)=0

⇒x=5,x=1

When x=5, we get y=7

When x=1, we get y=3

Coordinates of the end points of the chord intercepted by the given line and the given circle on (5,7) and (1,3).

∴ length of chord =  

(5−1)  

2

+(7−3)  

2

 

​  

=  

(4)  

2

+(4)  

2

 

​  

 

=  

32

​  

=4  

2

​