Column 1 has the condition on circle and column 2 has the equation of circles.which one of them are matched correct?
Column 1 column 2
1) Centre of origin and radius = 10 P) (x−8)(x+8)+(y−6)(y+6)=0
2) Extremeties of diameter are (8,6) and (-8,-6) Q) (x−6)(x+6)+(y−8)(y+8)=0
3) Centre is (1,-2) and radius is 4 R) x2 + y2 −2x + 4y − 11 = 0
1) Equation of circle with origin as centre and radius r is given by x2 + y2 = r2
⇒ x2 + y2 = 100 is the equation of the circle we will expand the equation given P and check if it gives same equation x2 + y2 = 100 .
(x−8)(x+8) + (y−6)y+6=0
⇒ x2 − 64 + y2 − 36 = 0
⇒ x2 + y2 = 100
So both of them give the same equation
2) Equation of circle with (x1,y1) and (x2,y2) as the extremeties of diameter is given by
(x−x1)(x,x2) + (y−y1)(y−y2)
⇒ (x−8) (x+8)+(y−6) (y+6)=0
⇒ (x2 + y2 = 100
We will expand Q and see it gives the same equation.
(x−6)(x+6)+(y−8)(y+8)=0
⇒ x2 + y2 = 100
⇒ 2 is correctly matched
3) Equation of a circle with centre (h,k) and radius r is given by
(x−h)2 + (y−k)2 = r2
⇒ (x−1)2 + (y+2)2 = 42
⇒ x2 + y2 −2x + 4y + 1 + 4 =16
⇒ x2 + y2 −2x + 4y − 11 = 0
⇒ 3 is correctly matched.