Question 36549
TIP:
2.IF X^2 OR Y^2 IS ONLY PRESENT ,IT COULD BE A PARABOLA.
2.) x2 – 4x – 8y = 12
COMPLETE SQUARE
(X^2-2*2X+2^2)-2^2=12+8Y
(X-2)^2=8Y+16=8(Y+2)
THIS IS THE EQN.OF A PARABOLA .STD EQN. IS
(X-H)^2=4A(Y-K),WHERE
(H,K) IS THE VERTEX....(2,-2) HERE.
4A=LATUS RECTUM =8 HERE...A=2
FOCUS IS (H+A,K).....(2+2,-2)=(4,-2)..HERE.
DIRECTRIX IS X-H+A=0...
X-2+2=0...OR....X=0..
AXIS IS Y-K =0..Y+2=0
{{{ graph( 500, 500, -20, 20, -20, 20,(x^2-4*x-12)/8  ) }}}