Question

What is the equation of a parabola with focus of (5,3) and directrix y=-3

Answer 1

x 2 − 10 x − 18 y − 2 = 0 Explanation: for any point ( x , y ) on the parabola the distance from ( x , y ) to the focus and directrix are equal ⇒ √ ( x − 5 ) 2 + ( y − 3 ) 2 = | y + 6 | squaring both sides ( x − 5 ) 2 + ( y − 3 ) 2 = ( y + 6 ) 2 ⇒ x 2 − 10 x + 25 + y 2 − 6 y + 9 = y 2 + 12 y + 36 ⇒ x 2 − 10 x − 18 y − 2 = 0