Answer to Question #149885 in Analytic Geometry for Dhruv rawat

Question #149885
Find the focus and equation of the latus rectum if x^2+ky=0, where k>0
1
Expert's answer
2020-12-17T07:28:39-0500

Comparing the given equation x2=kyx^2=-ky of parabola with standard equation x2=4ayx^2=-4ay , we obtain k=4ak=4a

    a=k/4\implies a = k/4


Focus of standard parabola is (0,a)(0,-a)

So, for the given parabola, focus is (0,k4)(0,-\frac{k}{4})



Equation of latus rectum is given by y=ay=-a


Hence for the given parabola, equation of latus rectum is, y=k4y=-\frac{k}{4}




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