At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Write eq in standard form of the parabola that satisfies f= (4,3) directix x=-1
so vertex would be = (1.5,3) ?
@jim_thompson5910 haha sorry for bugging you all day!
A faster way to do it is realize that we can pick a point on the directrix say d = (-1,3) and the f = (4,3) and then find the middle distance from -1 to 4 which is 1.5 so the v = (1.5,3)
I just need to write the equation now. Which i'm not sure how to do D:
mmm vertex looks good :)
it's horizontal so: 4p(x-h)=(y-k)^2 4p(x-1.5)=(y-3)^2 ?
how do I find p?
oh! p is the distance is from vertex to foci?
distance between focus and directrix was 5, ya? p is half of that. the value you used to find the vertex. yes.
so p = 2.5 yaya
how would I write that more attractively :P
is it ok to write it as y^2=10x-18 ?
or should I write it as y= +/- sqroot 10x+-18 ?
\[(x+1)^2=(x-4)2+(y-3)^2\] \[x^2+2x+1=x^2-8x+16+(y-3)^2\] \[x^2+2x+1-x^2+8x-16=(y-3)^2\] \[(y-3)^2=10x-15\]
@surjithayer we forgot the shift upwards. o.0
shift upwards? what? 0_o
That's what the y-3 is, ya?
the focal point is (4,3) so we know that it's not on the x = 0 line
but when I put the equation into a graphing thing it puts it on the x line
it does? 0_o https://www.desmos.com/calculator/wyivsbib3n looks ok to me.
hrrm I simplified it further and it was coming out wrong. Probably my calculations were wrong. Ok, all good. Thanks :)