Find an equation of largest sphere with center(5,4,9) that is contained in the first octant.

Such a sphere can have a radius of up to 4, so that its equation would be

Any larger radius would make the sphere cross the plane and it would no longer be contained in the first octant.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq