The focus of a parabola is (4,7) and the directrix is y=8. What is an equation of the parabola? (x−4)2=−4(y−9) (x−4)2=−2(y−7.5) (x−4)2=−0.5(y−7.5) (x−4)2=−(y−9)
Accepted Solution
A:
step 1 we need to find the distance between (x, y) and the focus (4,7) (x, y)-------> is any point on the parabola. d=√[(x-4)²+(y-7)²]
step 2 Find the distance between (x, y) and the directrix y=8 the distance is given by d=║(y-8)║
step 3 Equating the two expressions gives √[(x-4)²+(y-7)²]=║(y-8)║ Squaring both sides give (x-4)²+(y-7)²=(y-8)² Expand and simplify x²-8x+16+y²-14y+49=y²-16y+64 x²-8x+65=-2y+64 Complete
the square Remember to balance the equation x²-8x+16-16=-2y-1 (x²-8x+16)=-2y-1+16 Rewrite as perfect squares(x-4)²=-2y+15 (x-4)²=-2(y-15/2)------->(x-4)²=-2(y-7.5)