Question

a circle has its centre on the line x+y=2 and the circle intersects the line x=3 and y=2
find the length of diameter of the circle​

Answer 1

Answer:

you will find anwer in 7 th standard math textbook

Answer 2

Answer:

Pair of lines:

x2+2xy+3x+6y=0

⇒x(x+2y)+3(x+2y)=0

⇒(x+2y)(x+3)=0

⇒x+2y=0

and x+3=0

Are the two normals and their point of intersection must be the centre of the circle.

⇒x=−3

and y=2−x=23

⇒(−3,23) is the centre of required circle.

(∵x(x−4)+y(y−3)=0  is the diametric form of the circle. Hence, (0,0) and (4,3) are the diametric end points.)

⇒ Centre →(20+4,20+3)→(2,23)

radius =21(16+9)

=25

The required circle with centre (−3,23) is just sufficient to contain the circle

x(x−4)+y(y−3)=0

∴ radius of required circle

=distance between (−3,