Q.4 Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of X - axis and y axis respectively.
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Q.4 Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of X - axis and y axis respectively.Q.4 Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of X - axis and y axis respectively.Q.4 Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of X - axis and y axis respectively.Q.4 Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of X - axis and y axis respectively.
GiVeN,
Length of chord on x-axis = 4
Length of chord on y-axis = 6
We know that,
General equation of circle,
★x^2 +y^2 +2gx+2fy+c=0
✒ We observe that (0 , 0) , (4 , 0) & (0 , 6) are on circle, i.e. co-ordinates of the circle.
✔ So putting these points in the general equation we have,
☆ For point (0 , 0) :-
(0)^2+(0)^2 +2g×0+2f×0+c=0
⟼0+0+0+0+c=0
⟼c=0
☆ For point (4 , 0)
(4)^2+(0)^2+2g.4+2f.0+0=0
⟼16+0+8g+0+0=0
⟼8g=−16
⟼g= −16/8
⟼g=−2
☆For point (0 , 6) ;-
(0)^2+(6)^2 +2g.0+2f.6+0=0
⟼12f=−36
⟼f=−36/12
⟼f=−3
☆ Put the value of f , g & c in the equation of circle, we get
⟹x^2 +y^2+2.(−2).x+2.(−3).y+0=0
⟹x^2 +y^2 −4x−6y=0
⟹ x^2 +y^2 −4x−6y=0.