Question

i need help plss

Answer 1

curve is symmetrical about theta=pi/2

Answer 2

it is a circle with radius 3 and symmetrical about y-axis with center at (0,3)

Answer 3

We need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the hypotenuse is the distance between points A and C, which we can find using the distance formula:

distance AC = √[(xC - xA)^2 + (yC - yA)^2]
= √[(4 - (-2))^2 + (0 - 4)^2]
= √[6^2 + (-4)^2]
= √(36 + 16)
= √52
= 2√13

Now, we need to find the length of the shorter leg of the right triangle, which is the distance between points A and B. We can use the distance formula again:

distance AB = √[(xB - xA)^2 + (yB - yA)^2]
= √[(-2 - (-2))^2 + (4 - 0)^2]
= √0 + 16
= 4

Finally, we can use the Pythagorean theorem to find the length of the longer leg, which is the distance between points B and C:

distance BC = √(distance AC^2 - distance AB^2)
= √(52 - 16)
= √36
= 6

Therefore, the length of the segment BC is 6 units.