Conic Sections Question 536
Question: The equation of the latus rectum of the parabola represented by equation $ y^{2}+2Ax+2By+C=0 $ is
Options:
A) $ x=\frac{B^{2}+A^{2}-C}{2A} $
B) $ x=\frac{B^{2}-A^{2}+C}{2A} $
C) $ x=\frac{B^{2}-A^{2}-C}{2A} $
D) $ x=\frac{A^{2}-B^{2}-C}{2A} $
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Answer:
Correct Answer: B
Solution:
$ {{(y+B)}^{2}}=-2Ax-C+B^{2}=-2A( x+\frac{C}{2A}-\frac{B^{2}}{2A} ) $
Equation of latus rectum $ x+\lambda =0 $
Vertex $ =( \frac{-C+B^{2}}{2A},B ) $ , focus $ \equiv ( \frac{-C+B^{2}}{2A}-\frac{A}{2},B ) $
Equation of L.R. is $ x=\frac{-C+B^{2}}{2A}-\frac{A}{2}=\frac{B^{2}-A^{2}-C}{2A} $ .
BETA
