The equation of the latus rectum of the parabola represented by equation y 2-2 Ax -2 By - C -0 is A- x-B2-A2-C-2 AB- x-B2-A2-C-2 AC- x-B2-A2-C-2 AD- x-A2-B2-C-2 A

The correct option is C (y+B)^2= 2Ax C+ B^2= 2A ( x+C/2A B^2/2A ) Equation of latus rectum x + λ = 0 Vertex = ( C+B^2/2A,B ),Focus ≡ ( C+ B^2/2A A/2,B ...

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Standard XII

Mathematics

Latus Rectum of Hyperbola

The equation ...

Question

The equation of the latus rectum of the parabola represented by equation $y^{2} + 2 A x + 2 B y + C = 0$ is

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Solution

The correct option is C
$(y + B)^{2} = - 2 A x - C + B^{2} = - 2 A (x + \frac{C}{2 A} - \frac{B^{2}}{2 A})$
Equation of latus rectum $x + λ = 0$
Vertex $= (\frac{- C + B^{2}}{2 A}, B), F o c u s \equiv (\frac{- C + B^{2}}{2 A} - \frac{A}{2}, B)$
Equation of L.R is $x = \frac{- C + B^{2}}{2 a} - \frac{A}{2} = \frac{B^{2} - A^{2} - C}{2 A}$ .

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The equation of the latus rectum of the parabola represented by equation y2+2Ax+2By+C=0 is

The correct option is C (y+B)2=−2Ax−C+B2=−2A(x+C2A−B22A) Equation of latus rectum x+λ=0 Vertex =(−C+B22A,B),Focus≡(−C+B22A−A2,B) Equation of L.R is x=−C+B22a−A2=B2−A2−C2A.

The equation of the latus rectum of the parabola represented by equation $y^{2} + 2 A x + 2 B y + C = 0$ is