Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 10.

x^2/100 + y^2/256 = 1

Step-by-step explanation:

The standard form of an ellipse is (x-h)^2/a^2+(y-k)^2/b^2=1

a is the horizontal radius

b is the vertical radius

h is the shift to the right

k is the shift upward

h and k will be shifts left and downward respectively if they are negative.  Since the question doesn't mention any shifting we can just let them be 0 so everything is easier.  The problem states the  vertical axis is 16 and the horizontal axis is 10 so that means a = 10 and b = 16.  Now we just plug in.

(x-h)^2/a^2+(y-k)^2/b^2=1

a = 10

b = 16

h = 0

k = 0

x^2/10^2+y^2/16^2=1

x^2/100 + y^2/256 = 1

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it