Q.

If the verex  of a parabola is (4,3) and its directrix is 3x + 2y -7=0, then equation of latus  rectum of the parabola is 

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a

3x+2y-31=0

b

3x+2y-18=0 

c

3x+2y-8=0 

d

3x+2y-29=0 

answer is B.

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Detailed Solution

Given Directrix of parabola  is 3x+2y7=0 and  vertex of parabola=(4,3)  Latusrectum is parallel to directrix and  passing through  focus.   Slope of latus rectum =32   Let equation of latus reactum be y=-32x+c Distance between vertex to directrix=12 (Distance between latus rectum and directrix ) 12+6-79+4=1272-c1+(-32)2 22=7-2c 22=7-2c(2c>7) 2c=29 c=292 Equation of latusrectum is 3x+2y-29=0   

 

 

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