Let the shortest distance from ( a , 0 ) , 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 ce

Question

Let the shortest distance from ( a , 0 ) , 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 :

TestHub · Accepted Answer

Normal at P ​ y + t x = 2 t + t 3 ↑ ( a , 0 ) at = 2 t + t 3 a = 2 + t 2 R ( 2 + t 2 , 0 ) ​ ​ PR = 4 ⇒ 4 + 4 t 2 = 16 4 t 2 = 12 ⇒ t 2 = 3 a = 5 R ( 5 , 0 ) ​ Focus ( 1 , 0 ) ( 1 , 0 ) & ( 5 , 0 ) will be tha end pts. of diameter ⇒ Eg n of circle is ​ ( x − 1 ) ( x − 5 ) + y 2 = 0 x 2 + y 2 − 6 x + 5 = 0 ​

Mathematics - Parabola Question with Solution | TestHub

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