Two parabola's y2=4a(x-λ1) and x2=4a(y-λ2) always touch each other, λ1 and λ2 being variable parameters. Then their points of contact lie on a _
1) straight line
2) parabola
c) circle
d) hyperbola
1points of contact?
I don't know how we get that . There can be only one point of contact no? . u've said that , they touch each other .
then , assuming it's so .
let the point be (h,k) , then it satisfies both thus we get
k2 / (h-λ1) = h2/(k-λ2)
I'm getting a cubic ????? then my method must be wrong.
I;'ll simplify and try. But I think my method is worng.
suggestions any body?
1straight line??
i thnk they will touch only if λ1=λ2
mayb i m wrong bt they cant touch for all values
for example for a very large value of λ2 & veery small value of λ1 they cant touch
1i dont hav any rigorous method fr dat
bt for λ1=λ2 =λ its a straight line which is quite obvious
and i saw second 1 wth the help of graph