Circles

Write the Eqn:

The circle is tangent to the line $\displaystyle 5x+12y = 26$ & the center is at the origin.

(I specifically dont knw where the circle is perpendicular to a part of this line)

Parabola

Write the Eqn:

Length of the latus rectum is 10 and the parabola opens upward.

Thanks in advance :)