Find the coordinates of the focus,axis,the eq | vedclass

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(A) The given equation is $y^{2}=8x$.Comparing this with the standard equation of a parabola $y^{2}=4ax$,we get $4a=8$,which implies $a=2$.Since the e

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Focus: $(2, 0)$,Axis: $y=0$,Directrix: $x=-2$,Latus Rectum: $8$

Vedclass · Answer

(A) The given equation is $y^{2}=8x$.Comparing this with the standard equation of a parabola $y^{2}=4ax$,we get $4a=8$,which implies $a=2$.Since the equation is of the form $y^{2}=4ax$,the axis of symmetry is the $x$-axis (i.e.,$y=0$).The focus of the parabola is $(a, 0) = (2, 0)$.The equation of the directrix is $x=-a$,which is $x=-2$.The length of the latus rectum is $4a = 4 	imes 2 = 8$.

Find the coordinates of the focus,axis,the equation of the directrix,and the length of the latus rectum of the parabola $y^{2}=8x$.

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