Question

To derive the standard formula of a circle, a radius r is constructed as the hypotenuse of a right triangle as shown.

Answer 1

Center is (h,k) and point E is (x,y) . We have to find the length of the legs which are used to derive the standard formula of circle .

The length base of the right triangle is (x-h) units.And the length of the right triangle is (y-k) units .

And that's the required lengths of the legs.

Therefore correct options are fourth and last options .

Answer 2

Answer:

Step-by-step explanation:

Given is a picture of a circle with radius r.

Since D, the centre of the circle has coordinates (h,k) we have

x coordinate of D=h and y coordinate of D =k

The point E has (x,y) as coordinates

i.e. distance from y axis is x and distance from x axis is y

The right triangle formed has legs as DF and FE

FE = distance from x axis of E- distance from x axis of F

= difference in y coordinates = y-k

(SInce DF is parallel to x axis, y coordinates of F = k)

Similarly another leg

DF= x-h

Hence answers are

x-h and y-k