Find the focus, directrix and length of latus rectum of parabola:y²=2

1.	Find the focus, directrix and length of latus rectum of parabola:y²=2√3x
Answer» SOLUTION TO DETERMINE The focus, DIRECTRIX and LENGTH of LATUS rectum of parabola : y² = 2√3x EVALUATION Here the given equation of the parabola $\sf{ {y}^{2} = 2 \sqrt{3}x }$ Comparing with y² = 4ax we get $\displaystyle \sf{4a = 2 \sqrt{3} }$ $\displaystyle \sf{ \implies \: a = \frac{ \sqrt{3} }{2} }$ Hence the required coordinates of focus $\displaystyle \sf{ = ( a \:, \: 0)}$ $\displaystyle \sf{ = \bigg( \frac{ \sqrt{3} }{2} \: , \: 0 \bigg) }$ The required equation of directrix $\displaystyle \sf{ x + \frac{ \sqrt{3} }{2} \: = \: 0 }$ Length of the latus rectum = 4a unit $= \sf{2 \sqrt{3} \: \: \: unit}$ ━━━━━━━━━━━━━━━━ Learn more from Brainly :- 1. The length of the latus rectum of the parabola 13[(x-3)^2+(y-4)^2 )= (2x-3y+ 5)^2 is brainly.in/question/24980361 2. A hyperbola has its center at (3, 4), a VERTEX at the point (9, 4), and the length of its latus rectum is 3 units. brainly.in/question/30210645