jee-main 2025 Q18

jee-main · India · session1_23jan_shift2 Circles Circle Equation Derivation
Let the shortest distance from $( \mathrm { a } , 0 )$, $\mathrm { a } > 0$, to the parabola $y ^ { 2 } = 4 x$ be 4. Then the equation of the circle passing through the point $( a , 0 )$ and the focus of the parabola, and having its centre on the axis of the parabola is :
(1) $x ^ { 2 } + y ^ { 2 } - 10 x + 9 = 0$
(2) $x ^ { 2 } + y ^ { 2 } - 6 x + 5 = 0$
(3) $x ^ { 2 } + y ^ { 2 } - 4 x + 3 = 0$
(4) $x ^ { 2 } + y ^ { 2 } - 8 x + 7 = 0$
Let the shortest distance from $( \mathrm { a } , 0 )$, $\mathrm { a } > 0$, to the parabola $y ^ { 2 } = 4 x$ be 4. Then the equation of the circle passing through the point $( a , 0 )$ and the focus of the parabola, and having its centre on the axis of the parabola is :\\
(1) $x ^ { 2 } + y ^ { 2 } - 10 x + 9 = 0$\\
(2) $x ^ { 2 } + y ^ { 2 } - 6 x + 5 = 0$\\
(3) $x ^ { 2 } + y ^ { 2 } - 4 x + 3 = 0$\\
(4) $x ^ { 2 } + y ^ { 2 } - 8 x + 7 = 0$