Equation of circle centered at extremity of positive minor axis and passing through the focus (on positive x-axis) of the ellipse (x2/16)+(y2/9)=1 is

Question

Equation of circle centered at extremity of positive minor axis and passing through the focus (on positive x-axis) of the ellipse (x2/16)+(y2/9)=1 is (A) x2+y2-6 y-7=0 (B) x2+y2-6 y=0 (C) x2+y2-6 y-16=0 (D) x2+y2-3 x-3 y=0

Tardigrade Admin · Accepted Answer

Centre ≡(0,3) focus S ≡(√7, 0) radius =B S=4 ∴ its equation is x2+(y-3)2=42

Q. Equation of circle centered at extremity of positive minor axis and passing through the focus (on positive $x$ -axis) of the ellipse $\frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1$ is

$x^{2} + y^{2} - 6 y - 7 = 0$

$x^{2} + y^{2} - 6 y = 0$

$x^{2} + y^{2} - 6 y - 16 = 0$

$x^{2} + y^{2} - 3 x - 3 y = 0$

Centre $\equiv (0, 3)$ focus $S \equiv (7, 0)$
radius $= BS = 4$
$∴$ its equation is $x^{2} + (y - 3)^{2} = 4^{2}$

Q. Equation of circle centered at extremity of positive minor axis and passing through the focus (on positive x-axis) of the ellipse 16x2​+9y2​=1 is

x2+y2−6y−7=0

x2+y2−6y=0

x2+y2−6y−16=0

x2+y2−3x−3y=0