If y=2x is a chord of circle x2 +y2 -10x =0 .find the equation of circle with this chord as diameter
Answers
Answer:
x²+y²-2x-4y=0
Step-by-step explanation:
Equation of circle
x²+y²-10x=0 -----------(1)
Equation of chord
y = 2x -----------(2)
Putting y=2x in equation (1)
x²+(2x)²-10x=0
=> x²+4x²-10x=0
=> 5x²-10x= 0
=> 5x(x-2)=0
If x=0 y=2x
y=2(0)=0
y=0
If x-2=0 y=2x
x=2 y=2(2)=4
So coordinates of points of intersection of chord and given circle are (0,0) and (2,4)
Now ATQ given chord is diameter of reqired circle whose equation we have to find
Now equation of circle whose diameter end points coordinates are (x₁,y₁)and (x₂,y₂) is as follows
(x-x₁)(x-x₂)+(y-y₁)(y-y₂)=0
So equation of required circle
=>(x-0)(x-2)+(y-0)(y-4)=0
=> x²-2x+y²-4y=0
=> x²+y²-2x-4y=0
It is required equation of circle.
