If y = 2x is a chord of the circle x2 + y2 - 10x = 0, find the equation of the circle with this chord as diameter. Hence, find the length of the chord intercepted.
maths circles ml Agarwal class 11
Answers
Step-by-step explanation:
First we need to find the intersection point of the chord and the circle.
substitute Y = 2X in the equation of circle.
====> X^2 + 4(X)^2 - 10 X = 0
Hence solutions of the equation are X = 0 and X = 2
=====> points of intersection are (0,0) and (2,4)
now the distance between (0,0) and (2,4) = ✓20 = 2✓5.
=====> radius of the required circle = 2✓5 /2 = ✓5
therefore the equation of the circle with (0,0) and (2,4) is
= (X-0)(X-2) + (Y-0)(Y-4) = [✓5]^2
= (X-0)(X-2) + (Y-0)(Y-4) = 5
SOLVE THE ABOVE EQUATION TO GET THE REQUIRED EQUATION.
Answer:
Step-by-step explanation:
if it is chord to that circle , it will intersect at 2 points
x^2+y^2-10x=0
x^2+4x^2-10x =0
5x^2-10x=0
x(5x-10)=0
x=0,2
therefore y coordinate = 0,4
x^2+y-2*y-4 = 0
x^2+y^2-6y+8=0
length of chord bisected
=2root r^2-p^2
=2root 100-20
=2root 80
=8root 5